DO NOT EDIT--Changes must be made through “File info” UNIT 9 … · 2020-03-24 · LESSON 21.1 Volume of Prisms and Cylinders LESSON 21.2 Volume of Pyramids LESSON 21.3 Volume

MATH IN CAREERS

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Jewelry Maker A jewelry maker designs and creates jewelry Jewelry makers often employ geometric designs and shapes in their work and so they need a good understanding of geometry For example they must calculate volume and surface area to determine the amount of materials needed They can also use computer designing programs to help them with their design specifications Jewelry makers often need to calculate costs of materials and labor to determine production costs for their designs

If you are interested in a career as a jewelry maker you should study these mathematical subjects

bull Algebrabull Geometrybull Business Math

Research other careers that require knowing the geometry of three-dimensional objects Check out the career activity at the end of the unit to find out how jewelry makers use math

VolumeUNIT 9

MODULE 21Volume Formulas

Unit 9 1117

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Reading Start -Up

Visualize VocabularyUse the words and draw examples to complete the chart

Object Example

Understand VocabularyComplete the sentences using the preview words

1 A cone whose axis is perpendicular to its base is called a(n)

2 A prism that has at least one nonrectangular lateral face is called a(n)

Active Reading

Pyramid Create a Pyramid and organize the adjectives used to describe different objectsmdashright regular obliquemdashon each of its faces When listening to descriptions of objects look for these words and associate them with the object that follows

VocabularyReview Words area (aacuterea) composite figure (figura compuesta)

cone (cono)

cylinder (cilindro)

pyramid (piraacutemide)

sphere (esfera) volume (volume)

Preview Wordsapothem (apotema)oblique cylinder

(cilindro oblicuo)oblique prism

(prisma oblicuo)regular pyramid

(piraacutemide regular)right cone (cono recto)right cylinder (cilindro recto)right prism (prisma recto)

1118Unit 9

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REAL WORLD VIDEO Check out how volume formulas can be used to find the volumes of real-world objects including sinkholes

Volume Formulas

MODULE PERFORMANCE TASK PREVIEW

How Big Is That SinkholeIn 2010 a giant sinkhole opened up in a neighborhood in Guatemala and swallowed up the three-story building that stood above it In this module you will choose and apply an appropriate formula to determine the volume of this giant sinkhole

Essential Question How can you use volume formulas to solve real-world problems

21LESSON 211

Volume of Prisms and Cylinders

LESSON 212

Volume of Pyramids

LESSON 213

Volume of Cones

LESSON 214

Volume of Spheres

LESSON 215

Scale Factor

Module 21 1119

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YOUAre Readycopy

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bull Online Homeworkbull Hints and Helpbull Extra Practice

Write the equation for the area of a circle of radius r

Substitute the radius

Simplify

Complete these exercises to review skills you will need for this module

Area of a CircleExample 1 Find the area of a circle with radius equal to 5

A = π r 2

A = π (5) 2 A = 25π

Find each area

1 A circle with radius 4 2 A circle with radius 6

3 A circle with radius 3π 4 A circle with radius 2 _ π

Volume PropertiesExample 2 Find the number of cubes that are 1 cm 3 in size that fit into a cube of size 1 m 3

Notice that the base has a length and width of 1 m or 100 cm so its area is 1 m 2 or 10000 cm 2

The 1 m 3 cube is 1 m or 100 cm high so multiply the area of the base by the height to find the volume of 1000000 cm 3

Find the volume

5 The volume of a 1 km 3 body of water in m 3

6 The volume of a 1 ft 3 box in in 3

Volume of Rectangular PrismsExample 3 Find the volume of a rectangular prism with height 4 cm length 3 cm and width 5 cm

V = Bh

V = (3) (5) (4)

V = 60 cm 3

Find each volume

7 A rectangular prism with length 3 m width 4 m and height 7 m

8 A rectangular prism with length 2 cm width 5 cm and height 12 cm

Write the equation for the volume of a rectangular prism

The volume of a rectangular prism is the area of the base times the height

Simplify

Module 21 1120


A Bh

C

b

ℓ

A

B

C

D

A

B

C

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Name Class Date

Explore Developing a Volume FormulaAs shown at the left below

_ AB has length b and C is any point on line ℓ parallel to

_ AB The distance between the

line containing _ AB and line ℓ is h No matter where C is located on line ℓ the area of the resulting ABC is always

a constant equal to 1 __ 2 bh Similarly given a polygon and a plane R that is parallel to the plane containing the polygon suppose you choose a point on R and create a pyramid with the chosen point as the vertex and the polygon as the base Both the base area and the height of the pyramid remain constant as you vary the location of the vertex on R so it is reasonable to assume that the volume of the pyramid remains constant

Postulate

Pyramids that have equal base areas and equal heights have equal volumes

Consider a triangular pyramid with vertex A directly over vertex D of the base BCD This triangular pyramid A-BCD can be thought of as part of a triangular prism with EFA cong BCD Let the area of the base be B and let AD = h

A What is the volume of the triangular prism

Resource Locker

Module 21 1133 Lesson 2

212 Volume of PyramidsEssential Question How do you find the volume of a pyramid

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A

B

C

D

E

F

A

B

C

D

E

F

A

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D

E

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A

B

C

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B Draw _ EC on one face of the triangular prism Consider the three pyramids A-BCD A-EBC

and A-CFE Explain why the sum of the volumes of these three pyramids is equal to the volume of the prism

C _ EC is the diagonal of a rectangle so EBC cong CFE

Explain why pyramids A-EBC and A-CFE have the same volume Explain why pyramids C-EFA and A-BCD have the same volume

D A-CFE and C-EFA are two names for the same pyramid so you now have shown that the three pyramids that form the triangular prism all have equal volume Compare the volume of the pyramid A-BCD and the volume of the triangular prism Write the volume of pyramid A-BCD in terms of B and h



h

B1

B2

B3B4

16 cm

24 cm

24 cm

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Reflect

1 Explain how you know that the three pyramids that form the triangular prism all have the same volume

Explain 1 Finding the Volume of a Pyramid In the Explore you showed that the volume of a ldquowedge pyramidrdquo having its vertex directly over one of the vertices of the base is one-third the product of the base area and the height Now consider a general pyramid As shown in the figure a pyramid can be partitioned into nonoverlapping wedge pyramids by drawing a perpendicular from the vertex to the base The volume V of the given pyramid is the sum of the volumes of the wedge pyramids

That is V = 1 __ 3 B 1 h + 1 __ 3 B 2 h + 1 __ 3 B 3 h + 1 __ 3 B 4 h

Using the distributive property this may be rewritten as V = 1 __ 3 h ( B 1 + B 2 + B 3 + B 4 ) Notice that B 1 + B 2 + B 3 + B 4 = B where B is the base area of the given pyramid

So V = 1 __ 3 Bh

The above argument provides an informal justification for the following result

Volume of a Pyramid

The volume V of a pyramid with base area B and height h is given by V= 1 __ 3 Bh

Example 1 Solve a volume problem

A Ashton built a model square-pyramid with the dimensions shown What is the volume of the pyramid

The pyramid is composed of wooden blocks that are in the shape of cubes A block has the dimensions 4 cm by 4 by 4 cm How many wooden blocks did Ashton use to build the pyramid

bull Find the volume of the pyramid

The area of the base B is the area of the square with sides of length 24 cm So B = 576 cm 2

The volume V of the pyramid is 1 _ 3 Bh = 1 _ 3 576 16

So V = 3072 c m 3

bull Find the volume of an average block

The volume of a cube is given by the formula V = s 3 So the volume W of a wooden block is 64 c m 3

bull Find the approximate number of wooden blocks in the pyramid divide V by W So the number of blocks that Ashton used is 48


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15 cm25 cm

15 cm

146 m

230 m230 m

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B The Great Pyramid in Giza Egypt is approximately a square pyramid with the dimensions shown The pyramid is composed of stone blocks that are rectangular prisms An average block has dimensions 13 m by 13 m by 07 m Approximately how many stone blocks were used to build the pyramid Round to the nearest hundred thousand


The area of the base B is the area of the square with sides of length 230 m So

The volume V of the pyramid is 1 _ 3 Bh = 1 _ 3

So V asymp


The volume of a rectangular prism is given by the formula So the volume W of an

average block is

bull Find the approximate number of stone blocks in the pyramid divide

by So the approximate number of blocks is

Reflect

2 What aspects of the model in Part B may lead to inaccuracies in your estimate

3 Suppose you are told that the average height of a stone block 069 m rather than 07 m Would the increase or decrease your estimate of the total number of blocks in the pyramid Explain

Your Turn

4 A piece of pure silver in the shape of a rectangular pyramid with the dimensions shown has a mass of 197 grams What is the density of silver Round to the nearest tenth (Hint density = mass _____ volume )



15 ft

12 ft25 ft

30 cm12 cm

15 cm

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Explain 2 Finding the Volume of a Composite FigureYou can add or subtract to find the volume of composite figures

Example 2 Find the volume of the composite figure formed by a pyramid removed from a prism Round to the nearest tenth

A

bull Find the volume of the prismV = lwh = (25) (12) ( 15 ) = 4500 ft 3

bull Find the volume of pyramid Area of base B = (25) ( 12 ) = 300 ft 2

Volume of pyramid V = 1 _ 3 (300) (15) = 1500 ft 3

bull Subtract the volume of the pyramid from volume of the prism to find the volume of the composite figure

4500 - 1500 = 3000

So the volume of the composite figure is 3000 ft 3

B

bull Find the volume of the prism

V = lwh = (30) ( ) ( ) = ( ) cm 3


Area of base B = cm 2

Volume of pyramid V = 1 _ 3 ( ) ( ) = ( ) c m 3

bull Subtract volume of pyramid from volume of prism to find volume of composite figure

- =

So the volume of the composite figure is c m 3



5 ft

3 ft

10 ft

2 ft

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Your Turn

Find the volume of the composite figure Round to the nearest tenth

5 The composite figure is formed from two pyramids The base of each pyramid is a square with a side length of 6 inches and each pyramid has a height of 8 inches

6 The composite figure is formed by a rectangular prism with two square pyramids on top of it

Elaborate

7 Explain how the volume of a pyramid is related to the volume of a prism with the same base and height

8 If the length and width of a rectangular pyramid are doubled and the height stays the same how does the volume of the pyramid change Explain

9 Essential Question Check-In How do you calculate the volume of a pyramid



A B

C

GH

E F

D

P

81 mm

152 mm

125 mm17 in

6 in4 in

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Evaluate Homework and Practice

1 Compare the volume of a square pyramid to the volume of a square prism with the same base and height as the pyramid

2 Which of the following equations could describe a square pyramid Select all that apply

A 3Vh = B

B V = 1 _ 3 ℓwB

C w = 3V _ ℓh

D V _ B = h _ 3

E V = w 2 h _ 3

F 1 _ 3 = VBh

3 Justify Reasoning As shown in the figure polyhedron ABCDEFGH is a cube and P is any point on face EFGH Compare the volume of the pyramid PABCD and the volume of the cube Demonstrate how you came to your answer

Find the volume of the pyramid Round your answer to the nearest tenth

4 5



12 cm

12 cm

12 cm

18 cm

125 cm

75cm

25 cm

5 cm

4 cm

4radic3 cm

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6 Find the volume of a hexagonal pyramid with a base area of 25 ft 2 and a height of 9 ft

7 The area of the base of a hexagonal pyramid is 24 ______ tan 30deg cm 2 Find its volume


8 9

10 Given a square pyramid with a height of 21 ft and a volume of 3969 cubic feet find the length of one side of the square base Round to the nearest tenth

11 Consider a pyramid with height 10 feet and a square base with side length of 7 feet How does the volume of the pyramid change if the base stays the same and the height is doubled



10 cm

X

10 cm

15 m

1 m

15 cm

15 cm

25 cm

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12 Algebra Find the value of x if the volume of the pyramid shown is 200 cubic centimeters

13 Find the height of a rectangular pyramid with length 3 meters width 8 meters and volume 112 cubic meters

14 A storage container for grain is in the shape of a square pyramid with the dimensions shown

a What is the volume of the container in cubic centimeters

b Grain leaks from the container at a rate of 4 cubic centimeters per second Assuming the container starts completely full about how many hours does it take until the container is empty

15 A piece of pure copper in the shape of a rectangular pyramid with the dimensions shown has a mass of 1676 grams What is the density of copper Round to the nearest hundredth (Hint density = mass _

volume )



4 ft

7 ft7 ft

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16 Represent Real World Problems An art gallery is a 6 story square pyramid with base area 1 __ 2 acre (1 acre = 4840 yd 2 1 story asymp 10 ft) Estimate the volume in cubic yards and cubic feet

17 Analyze Relationships How would the volume of the pyramid shown change if each dimension were multiplied by 6 Explain how you found your answer

18 Geology A crystal is cut into a shape formed by two square pyramids joined at the base Each pyramid has a base edge length of 57 mm and a height of 3 mm What is the volume of the crystal to the nearest cubic millimeter

19 A roof that encloses an attic is a square pyramid with a base edge length of 45 feet and a height of 5 yards What is the volume of the attic in cubic feet In cubic yards

ge07sec10l07003a AB

3 mm

57 mm45 ft

ge07se_c10l07004a

5 yd



10 ft

V = (49)(10)12

= 245 ft3

7 ft

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HOT Focus on Higher Order Thinking

20 Explain the Error Describe and correct the error in finding the volume of the pyramid

21 Communicate Mathematical Ideas A pyramid has a square base and a height of 5 ft The volume of the pyramid is 60 ft 3 Explain how to find the length of a side of the pyramidrsquos base

22 Critical Thinking A rectangular pyramid has a base length of 2 a base width of x and a height of 3x Its volume is 512 cm 3 What is the area of the base



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Lesson Performance Task

Genna is making a puzzle using a wooden cube Shersquos going to cut the cube into three pieces The figure below shows the lines along which she plans to cut away the first piece The result will be a piece with four triangular sides and a square side (shaded)

1 Each cut Genna makes will begin at the upper left corner of the cube Write a rule describing where she drew the lines for the first piece

2 The figure below shows two of the lines along which Genna will cut the second piece Draw a cube and on it draw the two lines Genna drew Then using the same rule you used above draw the third line and shade the square base of the second piece

3 When Genna cut away the second piece of the puzzle the third piece remained Draw a new cube and then draw the lines that mark the edges of the third piece Shade the square bottom of the third piece

4 Compare the volumes of the three pieces Explain your reasoning

5 Explain how the model confirms the formula for the volume of a pyramid



Base of inscribedpyramid has 3 sides



O

rry

12

MxA B

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Name Class Date

Explore Developing a Volume FormulaYou can approximate the volume of a cone by finding the volumes of inscribed pyramids

A The base of a pyramid is inscribed in the circular base of the cone and is a regular n-gon Let O be the center of the conersquos base let r be the radius of the cone and let h be the height of the cone Draw radii from O to the vertices of the n-gon

Construct segment _ OM from O to the midpoint M of

_ AB How can you prove that

AOM cong BOM

B How is ang1 cong ang2

Resource Locker


213 Volume of ConesEssential Question How do you calculate the volumes of composite figures that include cones

DO NOT EDIT--Changes must be made through File info CorrectionKey=NL-DCA-D

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C How many triangles congruent to AOB surround point O to make up the n-gon that is the base of the pyramid How can this be used to find the angle measures of AOM and BOM

D In AOM sin ang1 = x _ r so x = rsin ang1 In AOM cos ang1 = y _ r so y = rcos ang1

Since ang1 has a known value rewrite x and y using substitution

E To write an expression for the area of the base of the pyramid first write an expression for the area of AOB

Area of AOB = 1 _ 2 sdot base sdot height

= 1 _ 2 sdot 2x sdot y

= xy

What is the area of AOB substituting the new values for x and y What is the area of the n triangles that make up the base of the pyramid

F Use the area of the base of the pyramid to find an equation for the volume of the pyramid



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Your expression for the pyramidrsquos volume includes the expression n sin ( 180deg _ n ) cos ( 180deg _ n ) Use a calculator as follows to discover what happens to this expression as n gets larger and larger

bull Enter the expression n sin ( 180deg _ n ) cos ( 180deg _ n ) as Y 1 using x for n

bull Go to the Table Setup menu and enter the values shown

bull View a table for the function and scroll down

What happens to the expression as n gets very large

If n sin ( 180deg _ n ) cos ( 180deg _ n ) gets closer to π as n becomes greater what happens to the entire expression for the volume of the inscribed pyramid How is the area of the circle related to the expression for the base

Reflect

1 How is the formula for the volume of a cone related to the formula for the volume of a pyramid

Explain 1 Finding the Volume of a ConeThe volume relationship for cones that you found in the Explore can be stated as the following formula

Volume of a Cone

The volume of a cone with base radius r and base area B = π r 2 and height h is given by V = 1 __ 3 Bh or by V = 1 __ 3 π r 2 h

You can use a formula for the volume of a cone to solve problems involving volume and capacity


DO NOT EDIT--Changes must be made through File infoCorrectionKey=NL-DCA-D

18 in

22 in

39 in

24 in

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Example 1 The figure represents a conical paper cup How many fluid ounces of liquid can the cup hold Round to the nearest tenth (Hint 1 in 3 asymp 0554 fl oz)

A Find the radius and height of the cone to the nearest hundredth

The radius is half of the diameter so r = 1 _ 2 (22 in) = 11 in

To find the height of the cone use the Pythagorean Theorem

r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324

h 2 = 203 so h asymp 142 in

B Find the volume of the cone in cubic inches

V = 1 _ 3 π r 2 h asymp 1 _ 3 π ( ) 2 ( ) asymp i n 3

C Find the capacity of the cone to the nearest tenth of a fluid ounce

i n 3 asymp i n 3 times 0554 fl oz _ 1 i n 3

asymp fl oz

Your Turn

Right after Cindy buys a frozen yogurt cone her friend Maria calls her and they talk for so long that the frozen yogurt melts before Cindy can eat it The cone has a slant height of 39 in and a diameter of 24 in If the frozen yogurt has the same volume before and after melting and when melted just fills the cone how much frozen yogurt did Cindy have before she talked to Maria to the nearest tenth of a fluid ounce

2 Find the radius Then use the Pythagorean Theorem to find the height of the cone

3 Find the volume of the cone in cubic inches

4 Find the capacity of the cone to the nearest fluid ounce



19 mm32 mm

16 mm

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Explain 2 Finding the Volume of a Composite FigureYou can find the volume of a composite figure using appropriate volume formulas for the different parts of the figure

Example 2 Find the volume of the composite figure Round to the nearest cubic millimeter

A Find the volume of the cylinder

First find the radius r = 1 _ 2 (16 mm) = 8 mm

V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3

B Find the volume of the cone

The height of the cone is h = mm - mm = mm

It has the same radius as the cylinder r = mm

V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3

C Find the total volume

Total volume = volume of cylinder + volume of cone

= m m 3 + m m 3

asymp m m 3

Reflect

5 Discussion A composite figure is formed from a cone and a cylinder with the same base radius and its volume can be calculated by multiplying the volume of the cylinder by a rational number a _

b What

arrangements of the cylinder and cone could explain this



43 cm

36 cm

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Your Turn

Making a cone-shaped hole in the top of a cylinder forms a composite figure so that the apex of the cone is at the base of the cylinder Find the volume of the figure to the nearest tenth

6 Find the volume of the cylinder

7 Find the volume of the figure

Elaborate

8 Could you use a circumscribed regular n-gon as the base of a pyramid to derive the formula for the volume of a cone Explain

9 Essential Question Check-In How do you calculate the volumes of composite figures that include cones



19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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1 Interpret the Answer Katherine is using a cone to fill a cylinder with sand If the radii and height are equal on both objects and Katherine fills the cone to the very top how many cones will it take to fill the cylinder with sand Explain your answer

Find the volume of the cone Round the answer to the nearest tenth

2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

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Find the volume of the cone Leave the answer in terms of π

5 6

Find the volume of the composite figures Round the answer to the nearest tenth

7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

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9 10

11 Match the dimensions of a cone on the left with its volume on the right

A radius 3 units height 7 units 25π ___ 6 units 3

B diameter 5 units height 2 units 240π units 3

C radius 28 units slant height 53 units 11760π units 3

D diameter 24 units slant height 13 units 21π units 3



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otog

raphyIm

agin

giSto

ckPhotocom

12 The roof of a grain silo is in the shape of a cone The inside radius is 20 feet and the roof is 10 feet tall Below the cone is a cylinder 30 feet tall with the same radius

a What is the volume of the silo

b If one cubic foot of wheat is approximately 48 pounds and the farmerrsquos crop consists of approximately 2 million pounds of wheat will all of the wheat fit in the silo

13 A cone has a volume of 18π in 3 Which are possible dimensions of the cone Select all that apply

A diameter 1 in height 18 in

B diameter 6 in height 6 in

C diameter 3 in height 6 in

D diameter 6 in height 3 in

E diameter 4 in height 135 in

F diameter 135 in height 4 in



6 ft

8 ft

10 ft 12 in

12 in

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14 The figure shows a water tank that consists of a cylinder and a cone How many gallons of water does the tank hold Round to the nearest gallon (Hint 1 ft 3 = 748 gal)

15 Roland is using a special machine to cut cones out of cylindrical pieces of wood The machine is set to cut out two congruent cones from each piece of wood leaving no gap in between the vertices of the cones What is the volume of material left over after two cones are cut out



x

x

x

8 in

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16 Algebra Develop an expression that could be used to solve for the volume of this solid for any value of x

17 Persevere in Problem Solving A juice stand sells smoothies in cone-shaped cups that are 8 in tall The regular size has a 4 in diameter The jumbo size has an 8 in diameter

a Find the volume of the regular size to the nearest tenth

b Find the volume of the jumbo size to the nearest tenth

c The regular size costs $125 What would be a reasonable price for the jumbo size Explain your reasoning

18 Find the volume of a cone with base area 36π ft 2 and a height equal to twice the radius

19 Find the base circumference of a cone with height 5 cm and volume 125π cm 3



12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

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20 Analyze Relationships Popcorn is available in two cups a square pyramid or a cone as shown The price of each cup of popcorn is the same Which cup is the better deal Explain

21 Make a Conjecture A cylinder has a radius of 5 in and a height of 3 in Without calculating the volumes find the height of a cone with the same base and the same volume as the cylinder Explain your reasoning

22 Analyze Relationships A sculptor removes a cone from a cylindrical block of wood so that the vertex of the cone is the center of the cylinderrsquos base as shown Explain how the volume of the remaining solid compares with the volume of the original cylindrical block of wood

23 Explain the Error Which volume is incorrect Explain the error



Zone 1

Zone 2

30deg30deg

3 m3 m

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Yoursquove just set up your tent on the first night of a camping trip that yoursquove been looking forward to for a long time Unfortunately mosquitoes have been looking forward to your arrival even more than you have When you turn on your flashlight you see swarms of themmdashan average of 800 mosquitoes per square meter in fact

Since yoursquore always looking for a way to use geometry you decide to solve a problem How many mosquitoes are in the first three meters of the cone of your flashlight (Zone 1 in the diagram) and how many are in the second three meters (Zone 2)

1 Explain how you can find the volume of the Zone 1 cone

2 Find the volume of the Zone 1 cone Write your answer in terms of π



5 How many more mosquitoes are there in Zone 2 than there are in Zone 1 Use 314 for π



r

r r

r

r

x

R

x

xr

r

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Name Class Date

Explore Developing a Volume FormulaTo find the volume of a sphere compare one of its hemispheres to a cylinder of the same height and radius from which a cone has been removed

A The region of a plane that intersects a solid figure is called a cross section To show that cross sections have the same area at every level use the Pythagorean Theorem to find a relationship between r x and R

B A cross section of the cylinder with the cone removed is a ring

To find the area of the ring find the area of the outer circle and of the inner circle Then subtract the area of the inner circle from the outer circle

Resource Locker


214 Volume of SpheresEssential Question How can you use the formula for the volume of a sphere to calculate the

volumes of composite figures

DO NOT EDIT--Changes must be made through File info CorrectionKey=NL-BCA-B

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C Find an expression for the volume of the cylinder with the cone removed

D Use Cavalierirsquos principle to deduce the volume of a sphere with radius r

Reflect

1 How do you know that the height h of the cylinder with the cone removed is equal to the radius r

2 What happens to the cross-sectional areas when x = 0 when x = r



72 ft

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Explain 1 Finding the Volume of a SphereThe relationship you discovered in the Explore can be stated as a volume formula

Volume of a Sphere

The volume of a sphere with radius r is given by V = 4 _ 3 π r 3

You can use a formula for the volume of a sphere to solve problems involving volume and capacity

Example 1 The figure represents a spherical helium-filled balloon This tourist attraction allows up to 28 passengers at a time to ride in a gondola suspended underneath the balloon as it cruises at an altitude of 500 ft How much helium to the nearest hundred gallons does the balloon hold Round to the nearest tenth (Hint 1 gal asymp 01337 ft 3 )

Step 1 Find the radius of the balloon

The radius is half of the diameter so r = 1 _ 2 (72 ft) = 36 ft

Step 2 Find the volume of the balloon in cubic feet

V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3

Step 3 Find the capacity of the balloon to the nearest gallon

ft 3 asymp ft 3 times 1 gal

_ 01337 ft 3

asymp gal

Your Turn

A spherical water tank has a diameter of 27 m How much water can the tank hold to the nearest liter (Hint 1000 L = 1 m3)

3 Find the volume of the tank in cubic meters

4 Find the capacity of the tank to the nearest liter



7 in

13 cm5 cm

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Example 2 Find the volume of the composite figure Round to the nearest cubic centimeter

Step 1 Find the volume of the hemisphere

Step 2 Find the height of the cone

h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =

Step 3 Find the volume of the cone

The cone has the same radius as the

hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3

Step 4 Find the total volume

Total volume = volume of hemisphere + volume of cone

= c m 3 + c m 3

asymp cm 3

Reflect

5 Is it possible to create a figure by taking a cone and removing from it a hemisphere with the same radius

Your Turn

6 A composite figure is a cylinder with a hemispherical hole in the top The bottom of the hemisphere is tangent to the base of the cylinder Find the volume of the figure to the nearest tenth



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Elaborate

7 Discussion Could you use an inscribed prism to derive the volume of a hemisphere Why or why not Are there any other ways you could approximate a hemisphere and what problems would you encounter in finding its volume

8 Essential Question Check-In A gumball is in the shape of a sphere with a spherical hole in the center How might you calculate the volume of the gumball What measurements are needed


1 Analyze Relationships Use the diagram of a sphere inscribed in a cylinder to describe the relationship between the volume of a sphere and the volume of a cylinder




Circumferenceof great circleis 14π cm

37 in11 ft

20 cm 1 m circle is 81π in2Area of great

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Find the volume of the sphere Round the answer to the nearest tenth

2 3 4

Find the volume of the sphere Leave the answer in terms of π

5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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yFind the volume of the composite figure Leave the answer in terms of π

8 9

Find the volume of the composite figure Round the answer to the nearest tenth

10 11



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12 Analyze Relationships Approximately how many times as great is the volume of a grapefruit with diameter 10 cm as the volume of a lime with diameter 5 cm

13 A bead is formed by drilling a cylindrical hole with a 2 mm diameter through a sphere with an 8 mm diameter Estimate the volume of the bead to the nearest whole

14 Algebra Write an expression representing the volume of the composite figure formed by a hemisphere with radius r and a cube with side length 2r



5 ft

20 in12 in

12 in

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15 One gallon of propane yields approximately 91500 BTU About how many BTUs does the spherical storage tank shown provide Round to the nearest million BTUs (Hint 1 f t 3 asymp 748 gal)

16 The aquarium shown is a rectangular prism that is filled with water You drop a spherical ball with a diameter of 6 inches into the aquarium The ball sinks causing the water to spill from the tank How much water is left in the tank Express your answer to the nearest tenth (Hint 1 in 3 asymp 000433 gal)

17 A sphere with diameter 8 cm is inscribed in a cube Find the ratio of the volume of the cube to the volume of the sphere

A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



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For Exercises 18ndash20 use the table Round each volume to the nearest billion π

Planet Diameter (mi) Mercury 3032

Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775

18 Explain the Error Margaret used the mathematics shown to find the volume of Saturn

V = 4 _ 3 π r 2 = 4 _ 3 π (74898) 2 asymp 4 _ 3 π (6000000000) asymp 8000000000π

Explain the two errors Margaret made then give the correct answer

19 The sum of the volumes of Venus and Mars is about equal to the volume of which planet

20 How many times as great as the volume of the smallest planet is the volume of the largest planet Round to the nearest thousand



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21 Make a Conjecture The bathysphere was an early version of a submarine invented in the 1930s The inside diameter of the bathysphere was 54 inches and the steel used to make the sphere was 15 inches thick It had three 8-inch diameter windows Estimate the volume of steel used to make the bathysphere

22 Explain the Error A student solved the problem shown Explain the studentrsquos error and give the correct answer to the problem

A spherical gasoline tank has a radius of 05 ft When filled the tank provides 446483 BTU How many BTUs does one gallon of gasoline yield Round to the nearest thousand BTUs and use the fact that 1 ft 3 asymp 748 gal

23 Persevere in Problem Solving The top of a gumball machine is an 18 in sphere The machine holds a maximum of 3300 gumballs which leaves about 43 of the space in the machine empty Estimate the diameter of each gumball

The volume of the tank is 4 __ 3 π r 3 = 4 __ 3 π (05) 3 ft 3 Multiplying by 748 shows that this is approximately 392 gal So the number of BTUs in one gallon of gasoline is approximately 446483 times 392 asymp 1750000 BTU



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For his science project Bizbo has decided to build a scale model of the solar system He starts with a grapefruit with a radius of 2 inches to represent Earth His ldquoEarthrdquo weighs 05 pounds

Find each of the following for Bizborsquos model Use the rounded figures in the table Round your answers to two significant figures Use 314 for π

1 the scale of Bizborsquos model 1 inch = miles

2 Earthrsquos distance from the Sun in inches and in miles

3 Neptunersquos distance from the Sun in inches and in miles

4 the Sunrsquos volume in cubic inches and cubic feet

5 the Sunrsquos weight in pounds and in tons (Note the Sunrsquos density is 026 times the Earthrsquos density)

Radius (mi) Distance from Sun (mi)

Earth 4 times 1 0 3 93 times 1 0 7

Neptune 15 times 1 0 4 28 times 1 0 9

Sun 43 times 1 0 5


DO NOT EDIT--Changes must be made through File info CorrectionKey=NL-ECA-E

IN2_MNLESE389847_U9M21L4indd 1170 42717 417 PM

0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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Explore Exploring Effects of Changing Dimensions on Perimeter and Area

Changes made to the dimensions of a figure can affect the perimeter and the area

Use the figure to investigate how changing one or more dimensions of the figure affect its perimeter and area

A Apply the transformation (x y) rarr (3x y) Find the perimeter and the area

Original Dimensions Dimensions after (x y) rarr (3x y)

P = 6 + 4 radic_

2 P =

A = 6 A =

B Apply the transformation (x y) rarr (x 3y) Find the perimeter and the area

Original Dimensions Dimensions after (x y) rarr (x 3y)

P = 6 + 4 radic_

2 P =

A = 6 A =

C Apply the transformation (x y) rarr (3x 3y) Find the perimeter and the area

Original Dimensions Dimensions after (x y) rarr (3x 3y)

P = 6 + 4 radic_

2 P =

A = 6 A =

215 Scale FactorEssential Question How does multiplying one or more of the dimensions of a figure affect its

attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect

1 Describe the changes that occurred in Steps A and B Did the perimeter or area change by a constant factor

2 Describe the changes that occurred in Step C Did the perimeter or area change by a constant factor

Explain 1 Describe a Non-Proportional Dimension ChangeIn a non-proportional dimension change you do not use the same factor to change each dimension of a figure

Example 1 Find the area of the figure

A Find the area of the parallelogram Then multiply the length by 2 and determine the new area Describe the changes that took place

B Find the area of the trapezoid Then multiply the height by 05 and determine the new area Describe the changes that took place

Original Figure A = 1 _ 2 ( b 1 + b 2 ) h =

Transformed Figure A = 1 _ 2 ( b 1 + b 2 ) h =

When the height of the trapezoid changes by a factor of the

area of the trapezoid changes by a factor of

Reflect

3 Discussion When a non-proportional change is applied to the dimensions of a figure does the perimeter change in a predictable way

Your Turn

4 Find the area of a triangle with vertices (-5 -2) (-5 7) and (3 1) Then apply the transformation (x y) rarr (x 4y) and determine the new area Describe the changes that took place

Original Figure Transformed Figure

A = bh = 6 sdot 5 = 30 ft 2 A = bh = 12 sdot 5 = 60 ft 2

When the length of the parallelogram changes by a factor of 2 the area changes by a factor of 2


DO NOT EDIT--Changes must be made through File infoCorrectionKey=NL-BCA-B

10 cm 4 cm

4

6

6

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5 Find the area of the figure Then multiply the width by 5 and determine the new area Describe the changes that took place

Explain 2 Describe a Proportional Dimension ChangeIn a proportional dimension change you use the same factor to change each dimension of a figure

Example 2 Find the area and perimeter of a circle

A Find the circumference and area of the circle Then multiply the radius by 3 and find the new circumference and area Describe the changes that took place

Original Figure C = 2π (4) = 8π

A = π (4) 2 = 16π

Transformed Figure C = 2π (12) = 24π

A = π (12) 2 = 144π

The circumference changes by a factor of 3 and the area changes by a factor of 9 or 3 2

B Find the perimeter and area of the figure Then multiply the length and height by 1 __ 3 and find the new perimeter and area Describe the changes that took place


P = P =

A = A =

The perimeter changes by a factor of and the area changes by a factor of

Reflect

6 Fill in the table to describe the effect on perimeter (or circumference) and area when the dimensions of a figure are changed proportionally

Effects of Changing Dimensions Proportionally

Change in Dimensions Perimeter or Circumference Area

All dimensions multiplied by a



12

12 ft

6 ft

3 in

4 in

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Ocean

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orbis

Your Turn

7 Find the circumference and area of the circle Then multiply the radius by 025 and find the new circumference and area Describe the changes that took place

Explain 3 Describe a Proportional Dimension Change for a Solid

In a proportional dimension change to a solid you use the same factor to change each dimension of a figure

Example 3 Find the volume of the composite solid

A A company is planning to create a similar version of this storage tank a cylinder with hemispherical caps at each end Find the volume and surface area of the original tank Then multiply all the dimensions by 2 and find the new volume and surface area Describe the changes that took place

The volume of the solid is V = π r 2 h + 4 __ 3 π r 3 and the surface area is S = 2πrh + 4π r 2

Original Solid Transformed Solid

V = π (3) 2 (12) + 4 _ 3 π (3) 3 = 144π cu ft V = π (6) 2 (24) + 4 _ 3 π (6) 3 = 1152π cu ft

S = 2π (3 sdot 12) + 4π (3) 2 = 108π sq ft S = 2π (6 sdot 24) + 4π (6) 2 = 432π sq ft

The volume changes by a factor of 8 and the surface area changes by a factor of 4

B A childrenrsquos toy is shaped like a hemisphere with a conical top A company decides to create a smaller version of the toy Find the volume and surface area of the original toy Then multiply all dimensions by 2 __ 3 and find the new volume and surface area Describe the changes that took place

The volume of the solid is V = 1 __ 3 π r 2 h + 2 __ 3 π r 3

and the surface area is S = πr radic_

r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in

The volume changes by a factor of and the surface area changes by a factor of



3 in

3 in

8 in

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Reflect

8 Fill in the table to describe the effect on surface area and volume when the dimensions of a figure are changed proportionally


Change in Dimensions Surface Area Volume


Your Turn

9 A farmer has made a scale model of a new grain silo Find the volume and surface area of the model Use the scale ratio 1 36 to find the volume and surface area of the silo Compare the volumes and surface areas relative to the scale ratio Be consistent with units of measurement

Elaborate

10 Two square pyramids are similar If the ratio of a pair of corresponding edges is a b what is the ratio of their volumes What is the ratio of their surface areas

11 Essential Question Check-In How is a non-proportional dimension change different from a proportional dimension change



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A trapezoid has the vertices (0 0) (4 0) (4 4) and (-3 4)

1 Describe the effect on the area if only the x-coordinates of the vertices are multiplied by 1 __ 2

2 Describe the effect on the area if only the y-coordinates of the vertices are multiplied by 1 __ 2

3 Describe the effect on the area if both the x- and y-coordinates of the vertices are multiplied by 1 __ 2

4 Describe the effect on the area if the x-coordinates are multiplied by 2 and y-coordinates are multiplied by 1 __ 2



12 m

21 m

24 in

9 in

6 ft

18 ft

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Describe the effect of the change on the area of the given figure

5 The height of the triangle is doubled 6 The height of a trapezoid with base lengths 12 cm and 8 cm and height 5 cm is multiplied by 1 __ 3

7 The base of the parallelogram is multiplied by 2 __ 3 8 Communicate Mathematical Ideas A triangle has vertices (1 5) (2 3) and (-1 -6) Find the effect that multiplying the height of the triangle by 4 has on the area of the triangle without doing any calculations Explain

Describe the effect of each change on the perimeter or circumference and the area of the given figure

9 The base and height of an isosceles triangle with base 12 in and height 6 in are both tripled

10 The base and height of the rectangle are both multiplied by 1 __ 2



2 yd

3 yd10 m

5 m

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11 The dimensions are multiplied by 5 12 The dimensions are multiplied by 3 _ 5

13 For each change check whether the change is non-proportional or proportionalA The height of a triangle is doubled proportional non-proportional

B All sides of a square are quadrupled proportional non-proportional

C The length of a rectangle is multiplied by 3 _ 4 proportional non-proportional

D The height of a triangular prism is tripled proportional non-proportional

E The radius of a sphere is multiplied by radic ― 5 proportional non-proportional

14 Tina and Kleu built rectangular play areas for their dogs The play area for Tinarsquos dog is 15 times as long and 15 times as wide as the play area for Kleursquos dog If the play area for Kleursquos dog is 60 square feet how big is the play area for Tinarsquos dog

15 A map has the scale 1 inch = 10 miles On the map the area of Big Bend National Park in Texas is about 125 square inches Estimate the actual area of the park in acres (Hint 1 square mile = 640 acres)

16 A restaurant has a weekly ad in a local newspaper that is 2 inches wide and 4 inches high and costs $3675 per week The cost of each ad is based on its area If the owner of the restaurant decided to double the width and height of the ad how much will the new ad cost

17 Suppose the dimensions of a triangle with a perimeter of 18 inches are doubled Find the perimeter of the new triangle in inches

A rectangular prism has vertices (0 0 0) (0 3 0) (7 0 0) (7 3 0) (0 0 6) (0 3 6) (7 0 6) and (7 3 6)

18 Suppose all the dimensions are tripled Find the new vertices

19 Find the effect of the change on the volume of the prism



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20 How would the effect of the change be different if only the height had been tripled

21 Analyze Relationships How could you change the dimensions of a parallelogram to increase the area by a factor of 5 if the parallelogram does not have to be similar to the original parallelogram if the parallelogram does have to be similar to the original parallelogram


22 Algebra A square has a side length of (2x + 5) cm

a If the side length is mulitplied by 5 what is the area of the new square

b Use your answer to part (a) to find the area of the original square without using the area formula Justify your answer

23 Algebra A circle has a diameter of 6 in If the circumference is multiplied by (x + 3) what is the area of the new circle Justify your answer

24 Communicate Mathematical Ideas The dimensions of a prism with volume V and surface area S are multiplied by a scale factor of k to form a similar prism Make a conjecture about the ratio of the surface area of the new prism to its volume Test your conjecture using a cube with an edge length of 1 and a scale factor of 2



768 pixels

1024 pixels

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On a computer screen lengths and widths are measured not in inches or millimeters but in pixels A pixel is the smallest visual element that a computer is capable of processing A common size for a large computer screen is 1024 times 768 pixels (Widths rather than heights are conventionally listed first) For the following assume yoursquore working on a 1024 times 768 screen

1 You have a photo measuring 640 times 300 pixels and you want to enlarge it proportionally so that it is as wide as the computer screen Find the measurements of the photo after it has been scaled up Explain how you found the answer

2 a Explain why you canrsquot enlarge the photo proportionally so that it is as tall as the computer screen

b Why canrsquot you correct the difficulty in (a) by scaling the width of the photo by a factor of 1024 divide 640 and the height by a factor of 768 divide 300

3 You have some square photos and you would like to fill the screen with them so there is no overlap and there are no gaps between photos Find the dimensions of the largest such photos you can use (all of them the same size) and find the number of photos Explain your reasoning




Volume = 1 cubic unit

axis

right cylinderright prism

area is B square units

height is 1 unit

axis


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Name Class Date

Explore Developing a Basic Volume FormulaThe volume of a three-dimensional figure is the number of nonoverlapping cubic units contained in the interior of the figure This prism is made up of 8 cubes each with a volume of 1 cubic centimeter so it has a volume of 8 cubic centimeters You can use this idea to develop volume formulas

In this activity yoursquoll explore how to develop a volume formula for a right prism and a right cylinder

A right prism has lateral edges that are perpendicular to the bases with faces that are all rectangles

A right cylinder has bases that are perpendicular to its center axis

A On a sheet of paper draw a quadrilateral shape Make sure the sides arenrsquot parallel Assume the figure has an area of B square units

B Use it as the base for a prism Take a block of Styrofoam and cut to the shape of the base Assume the prism has a height of 1 unit

How would changing the area of the base change the volume of the prism

Resource Locker


211 Volume of Prisms and CylindersEssential Question How do the formulas for the volume of a prism and cylinder relate to area

formulas that you already know


height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

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If the base has an area of B square units how many cubic units does the prism contain

Now use the base to build a prism with a height of h units

How much greater is the volume of this prism compared to the one with a height of 1

Reflect

1 Suppose the base of the prism was a rectangle of sides l and w Write a formula for the volume of the prism using l w and h

2 A cylinder has a circular base Use the results of the Explore to write a formula for the volume of a cylinder Explain what you did

Explain 1 Finding the Volume of a PrismThe general formula for the volume of a prism is V = B ∙ h With certain prisms the volume formula can include the formula for the area of the base

Volume of a Prism

The formula for the volume of a right rectangular prism with length ℓ width w and height h is V = ℓwh

The formula for the volume of a cube with edge length s is V = s 3



3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

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Example 1 Use volume formulas to solve real world problems

A A shark and ray tank at the aquarium has the dimensions shown Estimate the volume of water in gallons Use the conversion 1 gallon = 0134 f t 3

Step 1 Find the volume of the aquarium in cubic feet

V = ℓwh = (120) (60) (8) = 57600 f t 3

Step 2 Use the conversion factor 1 gallon

_ 0134 f t 3

to estimate

the volume of the aquarium in gallons

57600 f t 3 ∙ 1 gallon

_ 0134 f t 3

asymp 429851 gallons 1 gallon

_ 0134 f t 3

= 1


__ 833 pounds

to estimate the weight of the water

429851 gallons ∙ 833 pounds

__ 1 gallon

asymp 3580659 pounds 833 pounds

__ 1 gallon

= 1

The aquarium holds about 429851 in gallons The water in the aquarium weighs about 3580659 pounds

B Chemistry Ice takes up more volume than water This cubic container is filled to the brim with ice Estimate the volume of water once the ice melts

Density of ice 09167 gc m 3 Density of water 1 g cm 3

Step 1 Find the volume of the cube of ice

V = s 3 = = c m 3

Step 2 Convert the volume to mass using the conversion factor

g _

c m 3

c m 3 ∙ g _

c m 3 asymp g

Step 3 Use the mass of ice to find the volume of water Use the conversion factor

248 g ∙ asymp c m 3

Reflect

3 The general formula for the volume of a prism is V = B ∙ h Suppose the base of a prism is a parallelogram of length l and altitude h Use H as the variable to represent the height of the prism Write a volume formula for this prism



Volume = 8 cubic unitsEach cube has a

side of 2k

h

h

h

h

h

hh

h

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Your Turn

4 Find the volume of the figure 5 Find the volume of the figure

Explain 2 Finding the Volume of a CylinderYou can also find the volume of prisms and cylinders whose edges are not perpendicular to the base

Oblique Prism Oblique Cylinder

An oblique prism is a prism that has at least one non-rectangular lateral face

An oblique cylinder is a cylinder whose axis is not perpendicular to the bases

Cavalierirsquos Principle

If two solids have the same height and the same cross-sectional area at every level then the two solids have the same volume



B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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Example 2 To find the volume of an oblique cylinder or oblique prism use Cavalierirsquos Principle to find the volume of a comparable right cylinder or prism

A The height of this oblique cylinder is three times that of its radius What is the volume of this cylinder Round to the nearest tenth

Use Cavalierirsquos Principle to find the volume of a comparable right cylinder

Represent the height of the oblique cylinder h = 3r

Use the area of the base to find r π r 2 = 81π c m 2 so r = 9

Calculate the height h = 3r = 27 cm

Calculate the volume V = Bh = (81π) 27 asymp 68707

The volume is about 68707 cubic centimeters

B The height of this oblique square-based prism is four times that of side length of the base What is the volume of this prism Round to the nearest tenth

Calculate the height of the oblique prism

h = s where s is the length of the square base

Use the area of the base to find s

s 2 = c m 2

s = radic_

cm

Calculate the height

h = 4s = 4 cm

Your Turn

Find the volume

6 7

Calculate the volume

V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

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Explain 3 Finding the Volume of a Composite FigureRecall that a composite figure is made up of simple shapes that combine to create a more complex shape A composite three-dimensional figure is formed from prisms and cylinders You can find the volume of each separate figure and then add the volumes together to find the volume of the composite figure

Example 3 Find the volume of each composite figure

A Find the volume of the composite figure which is an oblique cylinder on a cubic base Round to the nearest tenth

The base area of the cylinder is B = π r 2 = π (5) 2 = 25π f t 2

The cube has side lengths equal to the diameter of the cylinderrsquos circular base s = 10

The height of the cylinder is h = 22 - 10 = 12 ft

The volume of the cube is V = s 3 = 1 0 3 = 1000 f t 3

The volume of the cylinder is V = Bh = (25π f t 2 ) (12 ft) asymp 9425 f t 3

The total volume of the composite figure is the sum of the individual volumes

V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3

B This periscope is made up of two congruent cylinders and two congruent triangular prisms each of which is a cube cut in half along one of its diagonals The height of each cylinder is 6 times the length of the radius Use the measurements provided to estimate the volume of this composite figure Round to the nearest tenth

Use the area of the base to find the radius B = π r 2

π r 2 = π so r = in

Calculate the height each cylinder

h = 6r = 6 ∙ = in

The faces of the triangular prism that intersect the cylinders are congruent squares The side length s of each square is the same as the diameter of the circle

s = d = 2 ∙ = in

The two triangular prisms form a cube What is the volume of this cube

V = s 3 = 3

= i n 3

Find the volume of the two cylinders V = 2 ∙ 36π ∙ = i n 3


V = i n 3 + i n 3 asymp i n 3


DO NOT EDIT--Changes must be made through ldquoFile infordquo CorrectionKey=NL-ECA-E



r1 r2

h

r

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hton

Mif

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t Pub

lishi

ng

Com

pan

y

Reflect

8 A pipe consists of two concentric cylinders with the inner cylinder hollowed out Describe how you could calculate the volume of the solid pipe Write a formula for the volume

Your Turn

9 This robotic arm is made up of two cylinders with equal volume and two triangular prisms for a hand The volume of each prism is 1 __ 2 r times 1 __ 3 r times 2r where r is the radius of the cylinderrsquos base What fraction of the total volume does the hand take up

Elaborate

10 If an oblique cylinder and a right cylinder have the same height but not the same volume what can you conclude about the cylinders

11 A right square prism and a right cylinder have the same height and volume What can you conclude about the radius of the cylinder and side lengths of the square base

12 Essential Question Check-In How does the formula for the area of a circle relate to the formula for the volume of a cylinder



84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

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hton Mifflin H

arcourt Publishin

g Com

pany

1 The volume of prisms and cylinders can be represented with Bh where B represents the area of the base Identify the type of figure shown and match the prism or cylinder with the appropriate volume formula

A V = (π r 2 ) h B V = ( 1 _ 2 bh) h C V = ℓwh

Find the volume of each prism or cylinder Round to the nearest hundredth

2 3

4 The area of the hexagonal base is ( 54 ______ tan 30deg ) m 2 Its height is 8 m

5 The area of the pentagonal base is ( 125 _____ tan 36deg ) m 2 Its height is 15 m

6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

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Miff

lin H

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urt P

ublis

hing

Com

pany

8 Multi-Step A vase in the shape of an oblique cylinder has the dimensions shown What is the volume of the vase in liters Round to the nearest thundredth (Hint Use the right triangle in the cylinder to find its height)

Find the volume of each composite figure Round to the nearest tenth

9 10

11 12 The two figures on each end combine to form a right cylinder




5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

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hton Mifflin H

arcourt Publishin

g Com

pany

13 Colin is buying dirt to fill a garden bed that is a 9 ft by 16 ft rectangle If he wants to fill it to a depth of 4 in how many cubic yards of dirt does he need Round to the nearest cubic yard If dirt costs $25 per y d 3 how much will the project cost

14 Persevere in Problem Solving A cylindrical juice container with a 3 in diameter has a hole for a straw that is 1 in from the side Up to 5 in of a straw can be inserted

a Find the height h of the container to the nearest tenth

b Find the volume of the container to the nearest tenth

c How many ounces of juice does the container hold (Hint 1 i n 3 asymp 055 oz)

15 Abigail has a cylindrical candle mold with the dimensions shown If Abigail has a rectangular block of wax measuring 15 cm by 12 cm by 18 cm about how many candles can she make after melting the block of wax Round to the nearest tenth

16 Algebra Find the volume of the three-dimensional figure in terms of x

17 One cup is equal to 144375 i n 3 If a 1-cup measuring cylinder has a radius of



10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

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17 One cup is equal to 144375 i n 3 If a 1-cup measuring cylinder has a radius of 2 in what is its height If the radius is 15 in what is its height Round to the nearest tenth

18 Make a Prediction A cake is a cylinder with a diameter of 10 in and a height of 3 in For a party a coin has been mixed into the batter and baked inside the cake The person who gets the piece with the coin wins a prize

a Find the volume of the cake Round to the nearest tenth

b Keka gets a piece of cake that is a right rectangular prism with a 3 in by 1 in base What is the probability that the coin is in her piece Round to the nearest hundredth


19 Multi-Step What is the volume of the three-dimensional object with the dimensions shown in the three views

20 Draw Conclusions You can use displacement to find the volume of an irregular object such as a stone Suppose a 2 foot by 1 foot tank is filled with water to a depth of 8 in A stone is placed in the tank so that it is completely covered causing the water level to rise by 2 in Find the volume of the stone




2 in

11 in

2 in2 in

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21 Analyze Relationships One juice container is a rectangular prism with a height of 9 in and a 3 in by 3 in square base Another juice container is a cylinder with a radius of 175 in and a height of 9 in Describe the relationship between the two containers


A full roll of paper towels is a cylinder with a diameter of 6 inches and a hollow inner cylinder with a diameter of 2 inches

1 Find the volume of the paper on the roll Explain your method

2 Each sheet of paper on the roll measures 11 inches by 11 inches by 1 __ 32 inch Find the volume of one sheet Explain how you found the volume

3 How many sheets of paper are on the roll Explain



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STUDY GUIDE REVIEW MODULE

21Key Vocabularyright prism (prisma recto)

right cylinder (cilindro recto)

oblique prism (prisma oblicuo)

oblique cylinder (cilindro oblicuo)

cross section (seccioacuten transversal)

Write the formula for the volume of a cylinder

Substitute

Simplify

Write the formula for the volume of a pyramid

Substitute

Simplify

Find the radius

Simplify

Write the formula for the volume of a cone

Substitute

Simplify

Essential Question How can you use volume formulasto solve real-world problems

KEY EXAMPLE (Lesson 211)

Find the volume of a cylinder with a base radius of 3 centimeters and a height of 5 centimeters Write an exact answer

V = π r 2 h

= π (3) 2 (5) = 45π c m 3


Find the volume of a square pyramid with a base side length of12 inches and a height of 7 inches

V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3


Find the volume of a cone with a base diameter of 16 feet and aheight of 18 feet Write an exact answer

r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3


Find the volume of a sphere with a radius of 30 miles Write an exact answer

V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas

Write the formula for the volume of a sphere

Substitute

Simplify

Module 21 1181 Study Guide Review

DO NOT EDIT--Changes must be made through ldquoFile infordquoCorrectionKey=NL-BCA-B

95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12

EXERCISESFind the volume of each figure Write an exact answer (Lessons 211ndash214)

1 2

3 4

5 6

7 One side of a rhombus measures 12 inches Two angles measure 60deg Find the perimeter and area of the rhombus Then multiply the side lengths by 3 Find the new perimeter and area Describe the changes that took place (Lesson 215)

MODULE PERFORMANCE TASK

How Big Is That SinkholeIn 2010 an enormous sinkhole suddenly appeared in the middle of a Guatemalan neighborhood and swallowed a three-story building above it The sinkhole has an estimated depth of about 100 feet

How much material is needed to fill the sinkhole Determine what information is needed to answer the question Do you think your estimate is more likely to be too high or too low

What are some material options for filling the sinkhole and how much would they cost Which material do you think would be the best choice

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age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

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211ndash215 Volume Formulas

Find the volume of the figure (Lessons 211ndash214)

1 An oblique cylinder next to a cube 2 A prism of volume 3 with a pyramid of the same height cut out

3 A cone with a square pyramid of the same height cut out The pyramid has height l and its square base has area l 2

4 A cube with sides of length s with the biggest sphere that fits in it cut out

ESSENTIAL QUESTION

5 How would you find the volume of an ice-cream cone with ice cream in it What measurements would you need



11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

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oughton Mifflin H


Assessment Readiness

Module 21Mixed review

1 A simplified model of a particular monument is a rectangular pyramid placed on top of a rectangular prism as shown The volume of the monument is 66 cubic feet Determine whether the given measurement could be the height of the monumentSelect Yes or No for AndashCA 10 feet Yes NoB 13 feet Yes NoC 15 feet Yes No

2 A standard basketball has a radius of about 47 inches Choose True or False for each statementA The diameter of the basketball is

about 25 inches True FalseB The volume of the basketball is

approximately 2776 i n 3 True FalseC The volume of the basketball is

approximately 4349 i n 3 True False

3 A triangle has a side of length 8 a second side of length 17 and a third side of length x Find the range of possible values for x

4 Find the approximate volume of the figure at right composed of a cone a cylinder and a hemisphere Explain how you found the values needed to compute the volume



IN2_MNLESE389847_U9M21MCindd 1184 42717 428 PM

A

C DB

40deg 40deg

A

BC

4y

0 4

x

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Com

pan

yAssessment readinessUNIT 9 MIXED REVIEW


1 Consider each congruence theorem below Can you use the theorem to determine whether ABC cong ABD

Select Yes or No for AndashC

A ASA Triangle Congruence Theorem Yes No

B SAS Triangle Congruence Theorem Yes No

C SSS Triangle Congruence Theorem Yes No

2 For each pyramid determine whether the statement regarding its volume is true

Select True or False for each statement

A A rectangular pyramid with ℓ = 3 mw = 4 m h = 7 m has volume 84 m 3 True False

B A triangular pyramid with base B = 14 ft 2 and h = 5 ft has volume 60 f t 2 True False

C A pyramid with the same base and heightof a prism has less volume True False

3 For each shape determine whether the statement regarding its volume is true


A A cone with base radius r = 5 inand h = 12 in has volume 100π i n 3 True False

B A sphere with radius r = 6 _ π m hasvolume 8

_ π 2

m 3 True False

C A sphere is composed of multiplecones with the same radius True False

4 DeMarcus draws ABC Then he translates it along the vector ⟨-4 -3⟩rotates it 180deg and reflects it across the x-axis

Choose True or False for each statement

A The final image of ABC is in Quadrant IV True False

B The final image of ABC is a right triangle True False

C DeMarcus will get the same result if he True Falseperforms the reflection followed by the translation and rotation

Unit 9 1185


3 cm

9 cmSALT

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5 A volleyball has a radius of about 8 inches A soccer ball has a radius of about 425 inches Determine whether each statement regarding the volume of each ball is true Select True or False for each statement

A The volume of the volleyball is about 6827π in3 True False

B The volume of the soccer ball is about 768π in3 True False

C The volume of the volleyball is about 375π times the volume of the soccer ball True False

6 A cone and a cylinder have the same height and base diameter Is each statement regarding the volume of each shape true Select True or False for each statement

A If the height is 8 cm and the base diameter is 6 cm the volume of the cone is 72π cm3 True False

B If the height is 6 cm and the base diameter is 4 cm the volume of the cylinder is 24π cm3 True False

C The volume of the cylinder is always 3 times the volume of the cone True False

7 A vase is in the shape of a cylinder with a height of 15 inches The vase holds 375π in3 of water What is the diameter of the base of the vase Show your work

8 A salt shaker is a cylinder with half a sphere on top The radius of the base of the salt shaker is 3 cm and the height of the cylindrical bottom is 9 cm as shown in the diagram

What is the volume of the salt shaker Explain how you got your answer

9 A cube is dilated by a factor of 4 By what factor does its volume increase Explain your reasoning

Unit 9 1186


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Performance Tasks10 A scientist wants to compare the volumes of two cylinders One is twice as

high and has a diameter two times as long as the other If the volume of the smaller cylinder is 30 c m 3 what is the volume of the larger cylinder

11 You are trying to pack in preparation for a trip and need to fit a collection of childrenrsquos toys in a box Each individual toy is a composite figure of four cubes and all of the toys are shown in the figure Arrange the toys in an orderly fashion so that they will fit in the smallest box possible Draw the arrangement What is the volume of the box if each of the cubes have side lengths of 10 cm

12 A carpenter has a wooden cone with a slant height of 16 inches and a diameter of 12 inches The vertex of the cone is directly above the center of its base He measures halfway down the slant height and makes a cut parallel to the base He now has a truncated cone and a cone half the height of the original

A He expected the two parts to weigh about the same but they donrsquot Which is heavier Why

B Find the ratio of the weight of the small cone to that of the

truncated cone Show your work

Unit 9 1187


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mAth in CAreers

model maker A jewelry maker creates a pendant out of glass by attaching two square-based pyramids at their bases to form an octahedron Each triangular face of the octahedron is an equilateral triangle

a Derive a formula for the volume of the pendant if the side length is a Show your work

b The jewelry maker wants to package the pendant in a cylindrical box What should be the smallest dimensions of the box if the pendant just fits inside in terms of a Explain how you determined your answer

c What is the volume of empty space inside the box Your answer should be in terms of a and rounded to two decimal places Show your work

Unit 9 1188


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Reading Start -Up

Visualize VocabularyUse the words and draw examples to complete the chart

Object Example

Understand VocabularyComplete the sentences using the preview words

1 A cone whose axis is perpendicular to its base is called a(n)

2 A prism that has at least one nonrectangular lateral face is called a(n)

Active Reading

Pyramid Create a Pyramid and organize the adjectives used to describe different objectsmdashright regular obliquemdashon each of its faces When listening to descriptions of objects look for these words and associate them with the object that follows

VocabularyReview Words area (aacuterea) composite figure (figura compuesta)

cone (cono)

cylinder (cilindro)

pyramid (piraacutemide)

sphere (esfera) volume (volume)

Preview Wordsapothem (apotema)oblique cylinder

(cilindro oblicuo)oblique prism

(prisma oblicuo)regular pyramid

(piraacutemide regular)right cone (cono recto)right cylinder (cilindro recto)right prism (prisma recto)

1118Unit 9

DO NOT EDIT--Changes must be made through ldquoFile infordquo CorrectionKey=NL-ACA-A

MODULEcopy

Hou

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iffl

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any

bull Im

age

Cre

dit

s copy

Stri

ng

er

Reut

ers

Cor

bis


Volume Formulas




21LESSON 211


LESSON 212

Volume of Pyramids

LESSON 213

Volume of Cones

LESSON 214

Volume of Spheres

LESSON 215

Scale Factor

Module 21 1119


YOUAre Readycopy

Hou

ghton M

ifflin Harcourt Pub

lishing C

omp

any




Simplify



A = π r 2

A = π (5) 2 A = 25π

Find each area






Find the volume




V = Bh

V = (3) (5) (4)

V = 60 cm 3

Find each volume





Simplify

Module 21 1120


A Bh

C

b

ℓ

A

B

C

D

A

B

C

D

E

F

R

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Name Class Date






Postulate




Resource Locker




A

B

C

D

E

F

A

B

C

D

E

F

A

B

C

D

E

F

A

B

C

D

E

F

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arcourt Publishin

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pany








h

B1

B2

B3B4

16 cm

24 cm

24 cm

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Reflect





So V = 1 __ 3 Bh


Volume of a Pyramid








So V = 3072 c m 3






15 cm25 cm

15 cm

146 m

230 m230 m

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Mark

Go

dd

ardiSto

ckPhotocom





So V asymp



average block is



Reflect



Your Turn




15 ft

12 ft25 ft

30 cm12 cm

15 cm

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A





4500 - 1500 = 3000


B


V = lwh = (30) ( ) ( ) = ( ) cm 3





- =




5 ft

3 ft

10 ft

2 ft

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Your Turn




Elaborate






A B

C

GH

E F

D

P

81 mm

152 mm

125 mm17 in

6 in4 in

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A 3Vh = B

B V = 1 _ 3 ℓwB

C w = 3V _ ℓh

D V _ B = h _ 3

E V = w 2 h _ 3

F 1 _ 3 = VBh



4 5



12 cm

12 cm

12 cm

18 cm

125 cm

75cm

25 cm

5 cm

4 cm

4radic3 cm

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arcourt Publishin

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pany




8 9





10 cm

X

10 cm

15 m

1 m

15 cm

15 cm

25 cm

copy H

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Mif

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pan

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volume )



4 ft

7 ft7 ft

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arcourt Publishin

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pany





ge07sec10l07003a AB

3 mm

57 mm45 ft

ge07se_c10l07004a

5 yd



10 ft

V = (49)(10)12

= 245 ft3

7 ft

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Mif

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Com

pan

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copy H

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arcourt Publishin

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pany













O

rry

12

MxA B

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Mif

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Com

pan

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Name Class Date





AOM cong BOM


Resource Locker




copy H

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arcourt Publishin

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pany







= xy





copy H

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Mif

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Com

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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

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r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

copy H

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pan

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

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arcourt Publishin

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pany

Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

copy H

oug

hton

Mif

flin

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cour

t Pub

lishi

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Com

pan

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

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arcourt Publishin

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pany


5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

copy H

oug

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Mif

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cour

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lishi

ng

Com

pan

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9 10








copy H

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hton Mifflin H

arcourt Publishin

g Com

pany bull

copyJenniferPh

otog

raphyIm

agin

giSto

ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

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Mif

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Com

pan

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x

x

x

8 in

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hton Mifflin H

arcourt Publishin

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pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Com

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Zone 1

Zone 2

30deg30deg

3 m3 m

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arcourt Publishin

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pany











r

r r

r

r

x

R

x

xr

r

copy H

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Mif

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Har

cour

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Com

pan

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Name Class Date





Resource Locker





copy H

oug

hton Mifflin H

arcourt Publishin

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pany



Reflect





72 ft

copy H

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Mif

flin

Har

cour

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lishi

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Com

pan

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

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arcourt Publishin

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h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

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Mif

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ng

Com

pan

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Elaborate









37 in11 ft


copy H

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arcourt Publishin

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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

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Mif

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lishi

ng

Com

pan


8 9


10 11



copy H

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arcourt Publishin

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pany bull Im

age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

copy H

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Com

pan

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

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Har

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Com

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mag

e C

red

its

copyRe

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n Pa

asse

nS

hutt

erst

ock









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oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

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arcourt Publishin

g Com

pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

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flin

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t Pub

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

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t Pub

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

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hton

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flin

Har

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

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arcourt Publishin

g Com

pany









copy H

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

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t Pub

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pan

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


MODULEcopy

Hou

ght

on M

iffl

in H

arco

urt P

ublis

hin

g C

omp

any

bull Im

age

Cre

dit

s copy

Stri

ng

er

Reut

ers

Cor

bis


Volume Formulas




21LESSON 211


LESSON 212

Volume of Pyramids

LESSON 213

Volume of Cones

LESSON 214

Volume of Spheres

LESSON 215

Scale Factor

Module 21 1119


YOUAre Readycopy

Hou

ghton M

ifflin Harcourt Pub

lishing C

omp

any




Simplify



A = π r 2

A = π (5) 2 A = 25π

Find each area






Find the volume




V = Bh

V = (3) (5) (4)

V = 60 cm 3

Find each volume





Simplify

Module 21 1120


A Bh

C

b

ℓ

A

B

C

D

A

B

C

D

E

F

R

copy H

oug

hton

Mif

flin

Har

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t Pub

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ng

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Name Class Date






Postulate




Resource Locker




A

B

C

D

E

F

A

B

C

D

E

F

A

B

C

D

E

F

A

B

C

D

E

F

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany








h

B1

B2

B3B4

16 cm

24 cm

24 cm

copy H

oug

hton

Mif

flin

Har

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t Pub

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ng

Com

pan

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Reflect





So V = 1 __ 3 Bh


Volume of a Pyramid








So V = 3072 c m 3






15 cm25 cm

15 cm

146 m

230 m230 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Mark

Go

dd

ardiSto

ckPhotocom





So V asymp



average block is



Reflect



Your Turn




15 ft

12 ft25 ft

30 cm12 cm

15 cm

copy H

oug

hton

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flin

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t Pub

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A





4500 - 1500 = 3000


B


V = lwh = (30) ( ) ( ) = ( ) cm 3





- =




5 ft

3 ft

10 ft

2 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn




Elaborate






A B

C

GH

E F

D

P

81 mm

152 mm

125 mm17 in

6 in4 in

copy H

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hton

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flin

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t Pub

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A 3Vh = B

B V = 1 _ 3 ℓwB

C w = 3V _ ℓh

D V _ B = h _ 3

E V = w 2 h _ 3

F 1 _ 3 = VBh



4 5



12 cm

12 cm

12 cm

18 cm

125 cm

75cm

25 cm

5 cm

4 cm

4radic3 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




8 9





10 cm

X

10 cm

15 m

1 m

15 cm

15 cm

25 cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

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y







volume )



4 ft

7 ft7 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





ge07sec10l07003a AB

3 mm

57 mm45 ft

ge07se_c10l07004a

5 yd



10 ft

V = (49)(10)12

= 245 ft3

7 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

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y







copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













O

rry

12

MxA B

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

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y

Name Class Date





AOM cong BOM


Resource Locker




copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany







= xy





copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

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y





V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

copy H

oug

hton

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flin

Har

cour

t Pub

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ng

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

9 10








copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull

copyJenniferPh

otog

raphyIm

agin

giSto

ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

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y





x

x

x

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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hton

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flin

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t Pub

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











r

r r

r

r

x

R

x

xr

r

copy H

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hton

Mif

flin

Har

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t Pub

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ng

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Name Class Date





Resource Locker





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Reflect





72 ft

copy H

oug

hton

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flin

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t Pub

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ng

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

oug

hton

Mif

flin

Har

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t Pub

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ng

Com

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Elaborate









37 in11 ft


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan


8 9


10 11



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

copy H

oug

hton

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flin

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cour

t Pub

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

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pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

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Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


YOUAre Readycopy

Hou

ghton M

ifflin Harcourt Pub

lishing C

omp

any




Simplify



A = π r 2

A = π (5) 2 A = 25π

Find each area






Find the volume




V = Bh

V = (3) (5) (4)

V = 60 cm 3

Find each volume





Simplify

Module 21 1120


A Bh

C

b

ℓ

A

B

C

D

A

B

C

D

E

F

R

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date






Postulate




Resource Locker




A

B

C

D

E

F

A

B

C

D

E

F

A

B

C

D

E

F

A

B

C

D

E

F

copy H

oug

hton Mifflin H

arcourt Publishin

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h

B1

B2

B3B4

16 cm

24 cm

24 cm

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So V = 1 __ 3 Bh


Volume of a Pyramid








So V = 3072 c m 3






15 cm25 cm

15 cm

146 m

230 m230 m

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oug

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arcourt Publishin

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pany bull Im

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redits copy

Mark

Go

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ckPhotocom





So V asymp



average block is



Reflect



Your Turn




15 ft

12 ft25 ft

30 cm12 cm

15 cm

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A





4500 - 1500 = 3000


B


V = lwh = (30) ( ) ( ) = ( ) cm 3





- =




5 ft

3 ft

10 ft

2 ft

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Elaborate






A B

C

GH

E F

D

P

81 mm

152 mm

125 mm17 in

6 in4 in

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A 3Vh = B

B V = 1 _ 3 ℓwB

C w = 3V _ ℓh

D V _ B = h _ 3

E V = w 2 h _ 3

F 1 _ 3 = VBh



4 5



12 cm

12 cm

12 cm

18 cm

125 cm

75cm

25 cm

5 cm

4 cm

4radic3 cm

copy H

oug

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8 9





10 cm

X

10 cm

15 m

1 m

15 cm

15 cm

25 cm

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volume )



4 ft

7 ft7 ft

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arcourt Publishin

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ge07sec10l07003a AB

3 mm

57 mm45 ft

ge07se_c10l07004a

5 yd



10 ft

V = (49)(10)12

= 245 ft3

7 ft

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copy H

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O

rry

12

MxA B

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copy H

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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

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r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

copy H

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

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19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

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5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

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9 10








copy H

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copyJenniferPh

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6 ft

8 ft

10 ft 12 in

12 in

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x

x

x

8 in

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12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

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r

r r

r

r

x

R

x

xr

r

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72 ft

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

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h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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37 in11 ft


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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



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Venus 7521

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mag

e C

red

its

copyRe

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hutt

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copy H

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Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect











Reflect


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10 cm 4 cm

4

6

6

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

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redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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Your Turn


Elaborate





copy H

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12 m

21 m

24 in

9 in

6 ft

18 ft

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2 yd

3 yd10 m

5 m

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arcourt Publishin

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copy H

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flin

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768 pixels

1024 pixels

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axis



height is 1 unit

axis


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Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

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2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

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arcourt Publishin

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10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

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ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






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String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

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oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


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Unit 9 1187


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mAth in CAreers





Unit 9 1188


A Bh

C

b

ℓ

A

B

C

D

A

B

C

D

E

F

R

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Name Class Date






Postulate




Resource Locker




A

B

C

D

E

F

A

B

C

D

E

F

A

B

C

D

E

F

A

B

C

D

E

F

copy H

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arcourt Publishin

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h

B1

B2

B3B4

16 cm

24 cm

24 cm

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Reflect





So V = 1 __ 3 Bh


Volume of a Pyramid








So V = 3072 c m 3






15 cm25 cm

15 cm

146 m

230 m230 m

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oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Mark

Go

dd

ardiSto

ckPhotocom





So V asymp



average block is



Reflect



Your Turn




15 ft

12 ft25 ft

30 cm12 cm

15 cm

copy H

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A





4500 - 1500 = 3000


B


V = lwh = (30) ( ) ( ) = ( ) cm 3





- =




5 ft

3 ft

10 ft

2 ft

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Elaborate






A B

C

GH

E F

D

P

81 mm

152 mm

125 mm17 in

6 in4 in

copy H

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A 3Vh = B

B V = 1 _ 3 ℓwB

C w = 3V _ ℓh

D V _ B = h _ 3

E V = w 2 h _ 3

F 1 _ 3 = VBh



4 5



12 cm

12 cm

12 cm

18 cm

125 cm

75cm

25 cm

5 cm

4 cm

4radic3 cm

copy H

oug

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arcourt Publishin

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8 9





10 cm

X

10 cm

15 m

1 m

15 cm

15 cm

25 cm

copy H

oug

hton

Mif

flin

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Com

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volume )



4 ft

7 ft7 ft

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arcourt Publishin

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ge07sec10l07003a AB

3 mm

57 mm45 ft

ge07se_c10l07004a

5 yd



10 ft

V = (49)(10)12

= 245 ft3

7 ft

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hton

Mif

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Com

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copy H

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O

rry

12

MxA B

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Com

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Name Class Date





AOM cong BOM


Resource Locker




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= xy





copy H

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Com

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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

copy H

oug

hton

Mif

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Har

cour

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Com

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

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pany


5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

copy H

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hton

Mif

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Har

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Com

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9 10








copy H

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arcourt Publishin

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copyJenniferPh

otog

raphyIm

agin

giSto

ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

copy H

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Mif

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Com

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x

x

x

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











r

r r

r

r

x

R

x

xr

r

copy H

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hton

Mif

flin

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Com

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Name Class Date





Resource Locker





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Reflect





72 ft

copy H

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hton

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t Pub

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ng

Com

pan

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

oug

hton

Mif

flin

Har

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ng

Com

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Elaborate









37 in11 ft


copy H

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arcourt Publishin

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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

oug

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Mif

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Har

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8 9


10 11



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arcourt Publishin

g Com

pany bull Im

age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

copy H

oug

hton

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Com

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

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copyRe

gie

n Pa

asse

nS

hutt

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ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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10 cm 4 cm

4

6

6

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

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Ocean

C

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Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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Elaborate





copy H

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12 m

21 m

24 in

9 in

6 ft

18 ft

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2 yd

3 yd10 m

5 m

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copy H

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768 pixels

1024 pixels

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axis



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height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

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2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

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Com

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9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

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10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

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ton

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ublis

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Com

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2 in

11 in

2 in2 in

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






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String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


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Unit 9 1187


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mAth in CAreers





Unit 9 1188


A

B

C

D

E

F

A

B

C

D

E

F

A

B

C

D

E

F

A

B

C

D

E

F

copy H

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h

B1

B2

B3B4

16 cm

24 cm

24 cm

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So V = 1 __ 3 Bh


Volume of a Pyramid








So V = 3072 c m 3






15 cm25 cm

15 cm

146 m

230 m230 m

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redits copy

Mark

Go

dd

ardiSto

ckPhotocom





So V asymp



average block is



Reflect



Your Turn




15 ft

12 ft25 ft

30 cm12 cm

15 cm

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A





4500 - 1500 = 3000


B


V = lwh = (30) ( ) ( ) = ( ) cm 3





- =




5 ft

3 ft

10 ft

2 ft

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Your Turn




Elaborate






A B

C

GH

E F

D

P

81 mm

152 mm

125 mm17 in

6 in4 in

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A 3Vh = B

B V = 1 _ 3 ℓwB

C w = 3V _ ℓh

D V _ B = h _ 3

E V = w 2 h _ 3

F 1 _ 3 = VBh



4 5



12 cm

12 cm

12 cm

18 cm

125 cm

75cm

25 cm

5 cm

4 cm

4radic3 cm

copy H

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8 9





10 cm

X

10 cm

15 m

1 m

15 cm

15 cm

25 cm

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volume )



4 ft

7 ft7 ft

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ge07sec10l07003a AB

3 mm

57 mm45 ft

ge07se_c10l07004a

5 yd



10 ft

V = (49)(10)12

= 245 ft3

7 ft

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copy H

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O

rry

12

MxA B

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Name Class Date





AOM cong BOM


Resource Locker




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= xy





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Volume of a Cone





18 in

22 in

39 in

24 in

copy H

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r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

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Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

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arcourt Publishin

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5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

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9 10








copy H

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copyJenniferPh

otog

raphyIm

agin

giSto

ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

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x

x

x

8 in

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12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

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r

r r

r

r

x

R

x

xr

r

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Name Class Date





Resource Locker





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72 ft

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

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h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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Elaborate









37 in11 ft


copy H

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arcourt Publishin

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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

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Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

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t Pub

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y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

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cour

t Pub

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pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

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hton

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flin

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Com

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

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arcourt Publishin

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pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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hton

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t Pub

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Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

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hton

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flin

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t Pub

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Com

pan

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2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

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hton

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flin

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t Pub

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pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


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oug

hton

Mif

flin

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cour

t Pub

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

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arcourt Publishin

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pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

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t Pub

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

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oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

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copy H

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

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redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

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Com

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

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hton

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flin

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ng

Com

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

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Mif

flin

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Com

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Unit 9 1187


copy H

oug

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arcourt Publishin

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mAth in CAreers





Unit 9 1188


h

B1

B2

B3B4

16 cm

24 cm

24 cm

copy H

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Reflect





So V = 1 __ 3 Bh


Volume of a Pyramid








So V = 3072 c m 3






15 cm25 cm

15 cm

146 m

230 m230 m

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Go

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ckPhotocom





So V asymp



average block is



Reflect



Your Turn




15 ft

12 ft25 ft

30 cm12 cm

15 cm

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A





4500 - 1500 = 3000


B


V = lwh = (30) ( ) ( ) = ( ) cm 3





- =




5 ft

3 ft

10 ft

2 ft

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Elaborate






A B

C

GH

E F

D

P

81 mm

152 mm

125 mm17 in

6 in4 in

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A 3Vh = B

B V = 1 _ 3 ℓwB

C w = 3V _ ℓh

D V _ B = h _ 3

E V = w 2 h _ 3

F 1 _ 3 = VBh



4 5



12 cm

12 cm

12 cm

18 cm

125 cm

75cm

25 cm

5 cm

4 cm

4radic3 cm

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8 9





10 cm

X

10 cm

15 m

1 m

15 cm

15 cm

25 cm

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volume )



4 ft

7 ft7 ft

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ge07sec10l07003a AB

3 mm

57 mm45 ft

ge07se_c10l07004a

5 yd



10 ft

V = (49)(10)12

= 245 ft3

7 ft

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copy H

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O

rry

12

MxA B

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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

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r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

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19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

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5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

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9 10








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copyJenniferPh

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6 ft

8 ft

10 ft 12 in

12 in

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x

x

x

8 in

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12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

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Zone 1

Zone 2

30deg30deg

3 m3 m

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r

r r

r

r

x

R

x

xr

r

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72 ft

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

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h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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37 in11 ft


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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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copyJasm

ina81iSto

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5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



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Venus 7521

Earth 7926

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Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








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copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

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6 ft

5 ft

12 in

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10 cm 4 cm

4

6

6

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

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redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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copy H

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12 m

21 m

24 in

9 in

6 ft

18 ft

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2 yd

3 yd10 m

5 m

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arcourt Publishin

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copy H

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768 pixels

1024 pixels

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axis



height is 1 unit

axis


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height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

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2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

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10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

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ough

ton

Miff

lin H

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ublis

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Com

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2 in

11 in

2 in2 in

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






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String

erReutersC

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Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


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Unit 9 1187


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mAth in CAreers





Unit 9 1188


15 cm25 cm

15 cm

146 m

230 m230 m

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arcourt Publishin

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pany bull Im

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redits copy

Mark

Go

dd

ardiSto

ckPhotocom





So V asymp



average block is



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Your Turn




15 ft

12 ft25 ft

30 cm12 cm

15 cm

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A





4500 - 1500 = 3000


B


V = lwh = (30) ( ) ( ) = ( ) cm 3





- =




5 ft

3 ft

10 ft

2 ft

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Your Turn




Elaborate






A B

C

GH

E F

D

P

81 mm

152 mm

125 mm17 in

6 in4 in

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A 3Vh = B

B V = 1 _ 3 ℓwB

C w = 3V _ ℓh

D V _ B = h _ 3

E V = w 2 h _ 3

F 1 _ 3 = VBh



4 5



12 cm

12 cm

12 cm

18 cm

125 cm

75cm

25 cm

5 cm

4 cm

4radic3 cm

copy H

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arcourt Publishin

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8 9





10 cm

X

10 cm

15 m

1 m

15 cm

15 cm

25 cm

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volume )



4 ft

7 ft7 ft

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ge07sec10l07003a AB

3 mm

57 mm45 ft

ge07se_c10l07004a

5 yd



10 ft

V = (49)(10)12

= 245 ft3

7 ft

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Mif

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Com

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copy H

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O

rry

12

MxA B

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Name Class Date





AOM cong BOM


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Com

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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

oug

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arcourt Publishin

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pany





r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

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arcourt Publishin

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Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

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arcourt Publishin

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5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

copy H

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Mif

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Com

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9 10








copy H

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copyJenniferPh

otog

raphyIm

agin

giSto

ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

copy H

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Com

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x

x

x

8 in

copy H

oug

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arcourt Publishin

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pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

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arcourt Publishin

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pany











r

r r

r

r

x

R

x

xr

r

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Name Class Date





Resource Locker





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72 ft

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Com

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

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hton

Mif

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Com

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Elaborate









37 in11 ft


copy H

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arcourt Publishin

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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

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Mif

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8 9


10 11



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arcourt Publishin

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age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

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flin

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mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

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cour

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ng

Com

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mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect


Your Turn







10 cm 4 cm

4

6

6

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y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

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Ocean

C

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Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

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pany










12 m

21 m

24 in

9 in

6 ft

18 ft

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flin

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2 yd

3 yd10 m

5 m

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oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

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flin

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768 pixels

1024 pixels

copy H

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axis



height is 1 unit

axis


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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

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2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

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ton

Miff

lin H

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Com

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9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

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10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

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Com

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2 in

11 in

2 in2 in

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

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redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


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Unit 9 1187


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mAth in CAreers





Unit 9 1188


15 ft

12 ft25 ft

30 cm12 cm

15 cm

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A





4500 - 1500 = 3000


B


V = lwh = (30) ( ) ( ) = ( ) cm 3





- =




5 ft

3 ft

10 ft

2 ft

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Elaborate






A B

C

GH

E F

D

P

81 mm

152 mm

125 mm17 in

6 in4 in

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A 3Vh = B

B V = 1 _ 3 ℓwB

C w = 3V _ ℓh

D V _ B = h _ 3

E V = w 2 h _ 3

F 1 _ 3 = VBh



4 5



12 cm

12 cm

12 cm

18 cm

125 cm

75cm

25 cm

5 cm

4 cm

4radic3 cm

copy H

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8 9





10 cm

X

10 cm

15 m

1 m

15 cm

15 cm

25 cm

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volume )



4 ft

7 ft7 ft

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ge07sec10l07003a AB

3 mm

57 mm45 ft

ge07se_c10l07004a

5 yd



10 ft

V = (49)(10)12

= 245 ft3

7 ft

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O

rry

12

MxA B

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AOM cong BOM


Resource Locker




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= xy





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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

oug

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arcourt Publishin

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r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

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Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

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arcourt Publishin

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5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

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9 10








copy H

oug

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arcourt Publishin

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pany bull

copyJenniferPh

otog

raphyIm

agin

giSto

ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

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x

x

x

8 in

copy H

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arcourt Publishin

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pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

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r

r r

r

r

x

R

x

xr

r

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Name Class Date





Resource Locker





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72 ft

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

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h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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Elaborate









37 in11 ft


copy H

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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

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Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

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Com

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mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

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flin

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

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arcourt Publishin

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pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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hton

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flin

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t Pub

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Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

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hton

Mif

flin

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t Pub

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Com

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2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

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flin

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768 pixels

1024 pixels

copy H

oug

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arcourt Publishin

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axis



height is 1 unit

axis


copy H

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flin

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

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arcourt Publishin

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pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

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arcourt Publishin

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pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

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urt P

ublis

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Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

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arcourt Publishin

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10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

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ton

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lin H

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ublis

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Com

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2 in

11 in

2 in2 in

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

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String

erReutersC

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Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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Com

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


copy H

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Unit 9 1187


copy H

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mAth in CAreers





Unit 9 1188


5 ft

3 ft

10 ft

2 ft

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Your Turn




Elaborate






A B

C

GH

E F

D

P

81 mm

152 mm

125 mm17 in

6 in4 in

copy H

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A 3Vh = B

B V = 1 _ 3 ℓwB

C w = 3V _ ℓh

D V _ B = h _ 3

E V = w 2 h _ 3

F 1 _ 3 = VBh



4 5



12 cm

12 cm

12 cm

18 cm

125 cm

75cm

25 cm

5 cm

4 cm

4radic3 cm

copy H

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8 9





10 cm

X

10 cm

15 m

1 m

15 cm

15 cm

25 cm

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Com

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volume )



4 ft

7 ft7 ft

copy H

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arcourt Publishin

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ge07sec10l07003a AB

3 mm

57 mm45 ft

ge07se_c10l07004a

5 yd



10 ft

V = (49)(10)12

= 245 ft3

7 ft

copy H

oug

hton

Mif

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Har

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Com

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O

rry

12

MxA B

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Name Class Date





AOM cong BOM


Resource Locker




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= xy





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Com

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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

copy H

oug

hton

Mif

flin

Har

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ng

Com

pan

y





V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

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19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

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5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

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9 10








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copyJenniferPh

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6 ft

8 ft

10 ft 12 in

12 in

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x

x

x

8 in

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12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

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r

r r

r

r

x

R

x

xr

r

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72 ft

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

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h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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37 in11 ft


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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

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Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








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copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

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8 in

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10 cm 4 cm

4

6

6

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

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Ocean

C

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Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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12 m

21 m

24 in

9 in

6 ft

18 ft

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2 yd

3 yd10 m

5 m

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768 pixels

1024 pixels

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height is h units

B

W

ℓ

h

S

S

Sh B

W

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S

Sh

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Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

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2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

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9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

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10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

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Miff

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ublis

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Com

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2 in

11 in

2 in2 in

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






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String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

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oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


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Unit 9 1187


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mAth in CAreers





Unit 9 1188


A B

C

GH

E F

D

P

81 mm

152 mm

125 mm17 in

6 in4 in

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A 3Vh = B

B V = 1 _ 3 ℓwB

C w = 3V _ ℓh

D V _ B = h _ 3

E V = w 2 h _ 3

F 1 _ 3 = VBh



4 5



12 cm

12 cm

12 cm

18 cm

125 cm

75cm

25 cm

5 cm

4 cm

4radic3 cm

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8 9





10 cm

X

10 cm

15 m

1 m

15 cm

15 cm

25 cm

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volume )



4 ft

7 ft7 ft

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ge07sec10l07003a AB

3 mm

57 mm45 ft

ge07se_c10l07004a

5 yd



10 ft

V = (49)(10)12

= 245 ft3

7 ft

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copy H

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O

rry

12

MxA B

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AOM cong BOM


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= xy





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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

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r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

copy H

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

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Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

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arcourt Publishin

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5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

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9 10








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copyJenniferPh

otog

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ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

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x

x

x

8 in

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arcourt Publishin

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12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

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arcourt Publishin

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r

r r

r

r

x

R

x

xr

r

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Name Class Date





Resource Locker





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72 ft

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

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pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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Elaborate









37 in11 ft


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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

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arcourt Publishin

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Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

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flin

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t Pub

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mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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mag

e C

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copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect


Your Turn







10 cm 4 cm

4

6

6

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

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arcourt Publishin

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pany bull Im

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redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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hton

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t Pub

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Reflect





Your Turn


Elaborate





copy H

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hton Mifflin H

arcourt Publishin

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12 m

21 m

24 in

9 in

6 ft

18 ft

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flin

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Com

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2 yd

3 yd10 m

5 m

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hton Mifflin H

arcourt Publishin

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pany
















copy H

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Com

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768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

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pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

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cour

t Pub

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Com

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

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arcourt Publishin

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

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hton Mifflin H

arcourt Publishin

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pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

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oug

hton Mifflin H

arcourt Publishin

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10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






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String

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44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


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Unit 9 1187


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mAth in CAreers





Unit 9 1188


12 cm

12 cm

12 cm

18 cm

125 cm

75cm

25 cm

5 cm

4 cm

4radic3 cm

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8 9





10 cm

X

10 cm

15 m

1 m

15 cm

15 cm

25 cm

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volume )



4 ft

7 ft7 ft

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ge07sec10l07003a AB

3 mm

57 mm45 ft

ge07se_c10l07004a

5 yd



10 ft

V = (49)(10)12

= 245 ft3

7 ft

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O

rry

12

MxA B

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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

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r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

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Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

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5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

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9 10








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copyJenniferPh

otog

raphyIm

agin

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ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

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x

x

x

8 in

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12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

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arcourt Publishin

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pany











r

r r

r

r

x

R

x

xr

r

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72 ft

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

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arcourt Publishin

g Com

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h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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37 in11 ft


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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

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Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








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Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect


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10 cm 4 cm

4

6

6

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

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redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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Your Turn


Elaborate





copy H

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12 m

21 m

24 in

9 in

6 ft

18 ft

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2 yd

3 yd10 m

5 m

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arcourt Publishin

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copy H

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flin

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768 pixels

1024 pixels

copy H

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arcourt Publishin

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axis



height is 1 unit

axis


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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

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2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

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lin H

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Com

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9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

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10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

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ough

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lin H

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ublis

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Com

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2 in

11 in

2 in2 in

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






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c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


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Unit 9 1187


copy H

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arcourt Publishin

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mAth in CAreers





Unit 9 1188


10 cm

X

10 cm

15 m

1 m

15 cm

15 cm

25 cm

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volume )



4 ft

7 ft7 ft

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arcourt Publishin

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ge07sec10l07003a AB

3 mm

57 mm45 ft

ge07se_c10l07004a

5 yd



10 ft

V = (49)(10)12

= 245 ft3

7 ft

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copy H

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O

rry

12

MxA B

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AOM cong BOM


Resource Locker




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Com

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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

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arcourt Publishin

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r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

copy H

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Com

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

copy H

oug

hton Mifflin H

arcourt Publishin

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Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

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arcourt Publishin

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5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

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9 10








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copyJenniferPh

otog

raphyIm

agin

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ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

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x

x

x

8 in

copy H

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arcourt Publishin

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12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

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arcourt Publishin

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pany











r

r r

r

r

x

R

x

xr

r

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Com

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Name Class Date





Resource Locker





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Reflect





72 ft

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Com

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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hton

Mif

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Elaborate









37 in11 ft


copy H

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arcourt Publishin

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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

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flin

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mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

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ng

Com

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mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

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flin

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cour

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Com

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

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flin

Har

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t Pub

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Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

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flin

Har

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t Pub

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Com

pan

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768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

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pany










axis



height is 1 unit

axis


copy H

oug

hton

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

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arcourt Publishin

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

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2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

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urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

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redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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hton

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


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Unit 9 1187


copy H

oug

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pany

mAth in CAreers





Unit 9 1188


4 ft

7 ft7 ft

copy H

oug

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arcourt Publishin

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pany





ge07sec10l07003a AB

3 mm

57 mm45 ft

ge07se_c10l07004a

5 yd



10 ft

V = (49)(10)12

= 245 ft3

7 ft

copy H

oug

hton

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flin

Har

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copy H

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O

rry

12

MxA B

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AOM cong BOM


Resource Locker




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= xy





copy H

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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

oug

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arcourt Publishin

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r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

copy H

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

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pany


5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

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9 10








copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull

copyJenniferPh

otog

raphyIm

agin

giSto

ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

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x

x

x

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

hton Mifflin H

arcourt Publishin

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pany











r

r r

r

r

x

R

x

xr

r

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Resource Locker





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Reflect





72 ft

copy H

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t Pub

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

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hton

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Elaborate









37 in11 ft


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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oug

hton

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t Pub

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8 9


10 11



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oug

hton Mifflin H

arcourt Publishin

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pany bull Im

age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

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pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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hton Mifflin H

arcourt Publishin

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Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

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hton

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flin

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t Pub

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ng

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

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t Pub

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ng

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

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hton

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flin

Har

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t Pub

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

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copy H

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

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redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

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flin

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t Pub

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

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t Pub

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ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

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y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


10 ft

V = (49)(10)12

= 245 ft3

7 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

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copy H

oug

hton Mifflin H

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O

rry

12

MxA B

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Name Class Date





AOM cong BOM


Resource Locker




copy H

oug

hton Mifflin H

arcourt Publishin

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= xy





copy H

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Har

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ng

Com

pan

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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y





V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

copy H

oug

hton

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flin

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

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9 10








copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull

copyJenniferPh

otog

raphyIm

agin

giSto

ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

copy H

oug

hton

Mif

flin

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t Pub

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Com

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x

x

x

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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hton

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











r

r r

r

r

x

R

x

xr

r

copy H

oug

hton

Mif

flin

Har

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t Pub

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ng

Com

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Name Class Date





Resource Locker





copy H

oug

hton Mifflin H

arcourt Publishin

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Reflect





72 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y


Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

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pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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37 in11 ft


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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

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Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

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nS

hutt

erst

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copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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10 cm 4 cm

4

6

6

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

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Ocean

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Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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12 m

21 m

24 in

9 in

6 ft

18 ft

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2 yd

3 yd10 m

5 m

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768 pixels

1024 pixels

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axis



height is 1 unit

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height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

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S

S

Sh

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

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2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

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Miff

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Com

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9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

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arcourt Publishin

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10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

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ublis

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Com

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2 in

11 in

2 in2 in

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






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44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

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oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


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Unit 9 1187


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mAth in CAreers





Unit 9 1188


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O

rry

12

MxA B

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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

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r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

copy H

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

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Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

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5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

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9 10








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copyJenniferPh

otog

raphyIm

agin

giSto

ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

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x

x

x

8 in

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12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

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r

r r

r

r

x

R

x

xr

r

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72 ft

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

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arcourt Publishin

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h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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Elaborate









37 in11 ft


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arcourt Publishin

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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

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arcourt Publishin

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pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

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hton

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flin

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cour

t Pub

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ng

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mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

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cour

t Pub

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ng

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y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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10 cm 4 cm

4

6

6

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

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arcourt Publishin

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pany bull Im

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redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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hton

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flin

Har

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t Pub

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Reflect





Your Turn


Elaborate





copy H

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hton Mifflin H

arcourt Publishin

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pany










12 m

21 m

24 in

9 in

6 ft

18 ft

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flin

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2 yd

3 yd10 m

5 m

copy H

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hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

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hton

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flin

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t Pub

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pan

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768 pixels

1024 pixels

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oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


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oug

hton

Mif

flin

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t Pub

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

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arcourt Publishin

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pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

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t Pub

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

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hton

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

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9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

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10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

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arcourt Publishin

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

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redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

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t Pub

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pan

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

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Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188





O

rry

12

MxA B

copy H

oug

hton

Mif

flin

Har

cour

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Name Class Date





AOM cong BOM


Resource Locker




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hton Mifflin H

arcourt Publishin

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= xy





copy H

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hton

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Com

pan

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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y





V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

copy H

oug

hton

Mif

flin

Har

cour

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

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arcourt Publishin

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5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

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flin

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9 10








copy H

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copyJenniferPh

otog

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6 ft

8 ft

10 ft 12 in

12 in

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x

x

x

8 in

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arcourt Publishin

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12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

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arcourt Publishin

g Com

pany











r

r r

r

r

x

R

x

xr

r

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72 ft

copy H

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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Elaborate









37 in11 ft


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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

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arcourt Publishin

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Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

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asse

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copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect


Your Turn







10 cm 4 cm

4

6

6

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

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redits copy

Ocean

C

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Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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Your Turn


Elaborate





copy H

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12 m

21 m

24 in

9 in

6 ft

18 ft

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2 yd

3 yd10 m

5 m

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arcourt Publishin

g Com

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copy H

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768 pixels

1024 pixels

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oug

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axis



height is 1 unit

axis


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Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

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hton Mifflin H

arcourt Publishin

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pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

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urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

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String

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44 ft10 ft

c

b

a

lradic2

Top View

copy H

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

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arcourt Publishin

g Com

pany













Unit 9 1186


copy H

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Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany







= xy





copy H

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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany





r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

copy H

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

copy H

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hton

Mif

flin

Har

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t Pub

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ng

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9 10








copy H

oug

hton Mifflin H

arcourt Publishin

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pany bull

copyJenniferPh

otog

raphyIm

agin

giSto

ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

copy H

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hton

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x

x

x

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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hton

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Har

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











r

r r

r

r

x

R

x

xr

r

copy H

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hton

Mif

flin

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ng

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Name Class Date





Resource Locker





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Reflect





72 ft

copy H

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t Pub

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ng

Com

pan

y


Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

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Elaborate









37 in11 ft


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

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8 9


10 11



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

copy H

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hton

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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oug

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arcourt Publishin

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pany













Unit 9 1186


copy H

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flin

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Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


copy H

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flin

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Reflect



Volume of a Cone





18 in

22 in

39 in

24 in

copy H

oug

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arcourt Publishin

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r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

copy H

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

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pany


5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

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9 10








copy H

oug

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copyJenniferPh

otog

raphyIm

agin

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ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

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x

x

x

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











r

r r

r

r

x

R

x

xr

r

copy H

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Name Class Date





Resource Locker





copy H

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Reflect





72 ft

copy H

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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Elaborate









37 in11 ft


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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

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mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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mag

e C

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its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

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arcourt Publishin

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pany bull Im

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redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

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12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

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flin

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2 yd

3 yd10 m

5 m

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hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

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flin

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768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

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axis



height is 1 unit

axis


copy H

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

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arcourt Publishin

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

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pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






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redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

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hton

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Com

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

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Unit 9 1186


copy H

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hton

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t Pub

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Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


18 in

22 in

39 in

24 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





r 2 + h 2 = (18) 2

(11) 2 + h 2 = (18) 2

121 + h 2 = 324






asymp fl oz

Your Turn







19 mm32 mm

16 mm

copy H

oug

hton

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flin

Har

cour

t Pub

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ng

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y





V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

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9 10








copy H

oug

hton Mifflin H

arcourt Publishin

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pany bull

copyJenniferPh

otog

raphyIm

agin

giSto

ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

copy H

oug

hton

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flin

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t Pub

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x

x

x

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











r

r r

r

r

x

R

x

xr

r

copy H

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hton

Mif

flin

Har

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t Pub

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ng

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Name Class Date





Resource Locker





copy H

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Reflect





72 ft

copy H

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t Pub

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ng

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

oug

hton

Mif

flin

Har

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t Pub

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ng

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Elaborate









37 in11 ft


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

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8 9


10 11



copy H

oug

hton Mifflin H

arcourt Publishin

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pany bull Im

age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

copy H

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hton

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

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y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

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Com

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






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String

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44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


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Unit 9 1187


copy H

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mAth in CAreers





Unit 9 1188


19 mm32 mm

16 mm

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V = π r 2 h = π (8) 2 (19) = 3820176 hellip m m 3




V = 1 _ 3 π r 2 h = 1 _ 3 π ( ) 2

( ) asymp m m 3



= m m 3 + m m 3

asymp m m 3

Reflect


b What




43 cm

36 cm

copy H

oug

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Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

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pany


5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

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9 10








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copyJenniferPh

otog

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ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

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x

x

x

8 in

copy H

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arcourt Publishin

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pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

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arcourt Publishin

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pany











r

r r

r

r

x

R

x

xr

r

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Name Class Date





Resource Locker





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Reflect





72 ft

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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Elaborate









37 in11 ft


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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

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arcourt Publishin

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pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

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e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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e C

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its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect


Your Turn







10 cm 4 cm

4

6

6

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

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pany bull Im

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redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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Your Turn


Elaborate





copy H

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12 m

21 m

24 in

9 in

6 ft

18 ft

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2 yd

3 yd10 m

5 m

copy H

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arcourt Publishin

g Com

pany
















copy H

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flin

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768 pixels

1024 pixels

copy H

oug

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arcourt Publishin

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axis



height is 1 unit

axis


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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

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arcourt Publishin

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

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arcourt Publishin

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

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9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

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arcourt Publishin

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redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

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flin

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t Pub

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ng

Com

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

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hton

Mif

flin

Har

cour

t Pub

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Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


43 cm

36 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn




Elaborate





19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

copy H

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hton

Mif

flin

Har

cour

t Pub

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9 10








copy H

oug

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arcourt Publishin

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copyJenniferPh

otog

raphyIm

agin

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ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

copy H

oug

hton

Mif

flin

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x

x

x

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











r

r r

r

r

x

R

x

xr

r

copy H

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hton

Mif

flin

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t Pub

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ng

Com

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Name Class Date





Resource Locker





copy H

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Reflect





72 ft

copy H

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t Pub

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ng

Com

pan

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

oug

hton

Mif

flin

Har

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t Pub

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ng

Com

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Elaborate









37 in11 ft


copy H

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arcourt Publishin

g Com

pany


2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

oug

hton

Mif

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Har

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t Pub

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8 9


10 11



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oug

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arcourt Publishin

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age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

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flin

Har

cour

t Pub

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ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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Com

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Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

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t Pub

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pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






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String

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orbis



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44 ft10 ft

c

b

a

lradic2

Top View

copy H

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

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hton

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flin

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Com

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


copy H

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Unit 9 1187


copy H

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arcourt Publishin

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mAth in CAreers





Unit 9 1188


19 mm

42 mm

59 ft

63 ft

20 cm

22 cm

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2 3

4



30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

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5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

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flin

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9 10








copy H

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copyJenniferPh

otog

raphyIm

agin

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ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

copy H

oug

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flin

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x

x

x

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

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arcourt Publishin

g Com

pany











r

r r

r

r

x

R

x

xr

r

copy H

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hton

Mif

flin

Har

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Name Class Date





Resource Locker





copy H

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Reflect





72 ft

copy H

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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Elaborate









37 in11 ft


copy H

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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

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8 9


10 11



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redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

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flin

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t Pub

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ng

Com

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y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

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mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

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Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

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flin

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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hton

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flin

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Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

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hton

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flin

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2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

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flin

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t Pub

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ng

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pan

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768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

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flin

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

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arcourt Publishin

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pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

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Mif

flin

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

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copy H

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flin

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

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t Pub

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ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

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Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


30 in

24 in

41 m

9 m

6 in

4 in 8 in

12 in

6 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


5 6


7 8



13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

copy H

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hton

Mif

flin

Har

cour

t Pub

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ng

Com

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9 10








copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull

copyJenniferPh

otog

raphyIm

agin

giSto

ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

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x

x

x

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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hton

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Har

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











r

r r

r

r

x

R

x

xr

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

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Name Class Date





Resource Locker





copy H

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Reflect





72 ft

copy H

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hton

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flin

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t Pub

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ng

Com

pan

y


Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

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Elaborate









37 in11 ft


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan


8 9


10 11



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

copy H

oug

hton

Mif

flin

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






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redits copy

String

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44 ft10 ft

c

b

a

lradic2

Top View

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oug

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

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flin

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t Pub

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Com

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

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hton

Mif

flin

Har

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Com

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y








Unit 9 1187


copy H

oug

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arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


13 m

2 m

1 m 12 ft

3 ft

5 ft10 ft

copy H

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9 10








copy H

oug

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pany bull

copyJenniferPh

otog

raphyIm

agin

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ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

copy H

oug

hton

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flin

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Com

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x

x

x

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

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hton

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











r

r r

r

r

x

R

x

xr

r

copy H

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hton

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flin

Har

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Name Class Date





Resource Locker





copy H

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Reflect





72 ft

copy H

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flin

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ng

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

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Elaborate









37 in11 ft


copy H

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arcourt Publishin

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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

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hton

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8 9


10 11



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redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

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y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

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mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

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hton Mifflin H

arcourt Publishin

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pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany bull Im

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redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

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12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

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flin

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t Pub

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2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

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flin

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t Pub

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768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

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flin

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

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arcourt Publishin

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

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flin

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

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hton Mifflin H

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

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String

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Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

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flin

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

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flin

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t Pub

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ng

Com

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

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Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull

copyJenniferPh

otog

raphyIm

agin

giSto

ckPhotocom













6 ft

8 ft

10 ft 12 in

12 in

copy H

oug

hton

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flin

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cour

t Pub

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x

x

x

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











r

r r

r

r

x

R

x

xr

r

copy H

oug

hton

Mif

flin

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t Pub

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ng

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Name Class Date





Resource Locker





copy H

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Reflect





72 ft

copy H

oug

hton

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flin

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cour

t Pub

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ng

Com

pan

y


Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

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Elaborate









37 in11 ft


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan


8 9


10 11



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

copy H

oug

hton

Mif

flin

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cour

t Pub

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ng

Com

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y




A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


6 ft

8 ft

10 ft 12 in

12 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y





x

x

x

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

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arcourt Publishin

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pany











r

r r

r

r

x

R

x

xr

r

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Resource Locker





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72 ft

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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Elaborate









37 in11 ft


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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

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arcourt Publishin

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Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

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Neptune 30775








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n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect


Your Turn







10 cm 4 cm

4

6

6

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

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Ocean

C

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Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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Your Turn


Elaborate





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12 m

21 m

24 in

9 in

6 ft

18 ft

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2 yd

3 yd10 m

5 m

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arcourt Publishin

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copy H

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768 pixels

1024 pixels

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axis



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axis


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height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

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2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

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ton

Miff

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Com

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9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

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10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

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ublis

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Com

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2 in

11 in

2 in2 in

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






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String

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Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


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Unit 9 1187


copy H

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mAth in CAreers





Unit 9 1188


x

x

x

8 in

copy H

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arcourt Publishin

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pany










12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

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arcourt Publishin

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r

r r

r

r

x

R

x

xr

r

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Resource Locker





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72 ft

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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Elaborate









37 in11 ft


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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

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Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

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flin

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e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

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flin

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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Com

pan

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Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

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pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

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hton

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flin

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Com

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2 yd

3 yd10 m

5 m

copy H

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hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

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hton

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flin

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768 pixels

1024 pixels

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oug

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arcourt Publishin

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axis



height is 1 unit

axis


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oug

hton

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flin

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

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arcourt Publishin

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pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

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cour

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

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Har

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Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

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arcourt Publishin

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copy H

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

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String

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Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

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flin

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t Pub

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ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


12 cm12 cm

20 cm

= _______1088π3

cm3

( 82π)( 17)__13=V V

= cm3

( 82π)( 15)__13=

320π8 cm

17 cm

15 cmA B

copy H

oug

hton

Mif

flin

Har

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t Pub

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Com

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Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











r

r r

r

r

x

R

x

xr

r

copy H

oug

hton

Mif

flin

Har

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ng

Com

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Name Class Date





Resource Locker





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arcourt Publishin

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Reflect





72 ft

copy H

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hton

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t Pub

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ng

Com

pan

y


Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

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Elaborate









37 in11 ft


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan


8 9


10 11



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oug

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arcourt Publishin

g Com

pany bull Im

age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

copy H

oug

hton

Mif

flin

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t Pub

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ng

Com

pan

y




A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

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e C

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its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect


Your Turn







10 cm 4 cm

4

6

6

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

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arcourt Publishin

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redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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Your Turn


Elaborate





copy H

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12 m

21 m

24 in

9 in

6 ft

18 ft

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2 yd

3 yd10 m

5 m

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arcourt Publishin

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copy H

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768 pixels

1024 pixels

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axis



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axis


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Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

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flin

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

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2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

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urt P

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hing

Com

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9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

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urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

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String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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Com

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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arcourt Publishin

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pany













Unit 9 1186


copy H

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Unit 9 1187


copy H

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mAth in CAreers





Unit 9 1188


Zone 1

Zone 2

30deg30deg

3 m3 m

copy H

oug

hton Mifflin H

arcourt Publishin

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pany











r

r r

r

r

x

R

x

xr

r

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Resource Locker





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72 ft

copy H

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

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hton

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Elaborate









37 in11 ft


copy H

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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

oug

hton

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8 9


10 11



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oug

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copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

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flin

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cour

t Pub

lishi

ng

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y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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Reflect


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10 cm 4 cm

4

6

6

copy H

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hton

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flin

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t Pub

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

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flin

Har

cour

t Pub

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pan

y











768 pixels

1024 pixels

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oug

hton Mifflin H

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axis



height is 1 unit

axis


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oug

hton

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Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

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arcourt Publishin

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

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y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

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redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


r

r r

r

r

x

R

x

xr

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

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Name Class Date





Resource Locker





copy H

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Reflect





72 ft

copy H

oug

hton

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t Pub

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ng

Com

pan

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

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Elaborate









37 in11 ft


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan


8 9


10 11



copy H

oug

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arcourt Publishin

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pany bull Im

age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

copy H

oug

hton

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

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hton

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flin

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

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Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

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copy H

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

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String

erReutersC

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Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

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hton

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flin

Har

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t Pub

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ng

Com

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

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hton

Mif

flin

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Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


copy H

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g Com

pany



Reflect





72 ft

copy H

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Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

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hton

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flin

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Elaborate









37 in11 ft


copy H

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pany


2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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Com

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8 9


10 11



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pany bull Im

age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

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flin

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t Pub

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ng

Com

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mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

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ng

Com

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y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

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hton

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flin

Har

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ng

Com

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

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flin

Har

cour

t Pub

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Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

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t Pub

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ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

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t Pub

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Com

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

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arcourt Publishin

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pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

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y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

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hton

Mif

flin

Har

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t Pub

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany









copy H

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hton

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flin

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

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pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


72 ft

copy H

oug

hton

Mif

flin

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cour

t Pub

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ng

Com

pan

y


Volume of a Sphere







V = 4 _ 3 π r 3

= 4 _ 3 π ( ) 3

asymp ft 3



_ 01337 ft 3

asymp gal

Your Turn






7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Elaborate









37 in11 ft


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan


8 9


10 11



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

copy H

oug

hton

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flin

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ng

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


7 in

13 cm5 cm

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany





h 2 + ( ) 2

= ( ) 2

h 2 + =

h 2 =

h =



hemisphere r = cm

V = 1 _ 3 π r 2 h

= 1 _ 3 π ( ) 2 ( ) = c m 3



= c m 3 + c m 3

asymp cm 3

Reflect


Your Turn




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37 in11 ft


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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

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arcourt Publishin

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Venus 7521

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oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

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copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

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8 in

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10 cm 4 cm

4

6

6

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

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Ocean

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r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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Elaborate





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12 m

21 m

24 in

9 in

6 ft

18 ft

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2 yd

3 yd10 m

5 m

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arcourt Publishin

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copy H

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768 pixels

1024 pixels

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axis



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height is h units

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W

ℓ

h

S

S

Sh B

W

ℓ

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S

Sh

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

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hton Mifflin H

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

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Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

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2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

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Com

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9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

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urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

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String

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44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


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Unit 9 1187


copy H

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arcourt Publishin

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mAth in CAreers





Unit 9 1188


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Elaborate









37 in11 ft


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2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

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8 9


10 11



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5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

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arcourt Publishin

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Venus 7521

Earth 7926

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Neptune 30775








copy H

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copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

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flin

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ng

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y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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10 cm 4 cm

4

6

6

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flin

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ng

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pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany bull Im

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redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

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Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

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hton

Mif

flin

Har

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2 yd

3 yd10 m

5 m

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hton Mifflin H

arcourt Publishin

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copy H

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hton

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flin

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768 pixels

1024 pixels

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hton Mifflin H

arcourt Publishin

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axis



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axis


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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

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arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany









copy H

oug

hton

Mif

flin

Har

cour

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188



37 in11 ft


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany


2 3 4


5 6 7



2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan


8 9


10 11



copy H

oug

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arcourt Publishin

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age C

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ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

copy H

oug

hton

Mif

flin

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ng

Com

pan

y




A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

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flin

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

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erReutersC

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44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

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hton

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flin

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ng

Com

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

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Mif

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Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

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mAth in CAreers





Unit 9 1188


2 ft5 ft 8 in

3 in

2 in

10 cm8 cm

3 cm

4 cm

24 mm

8 mm

10 mm

copy H

oug

hton

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flin

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cour

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8 9


10 11



copy H

oug

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pany bull Im

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redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

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A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

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mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

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Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

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flin

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Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

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t Pub

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Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

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pany










12 m

21 m

24 in

9 in

6 ft

18 ft

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hton

Mif

flin

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cour

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y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

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flin

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768 pixels

1024 pixels

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arcourt Publishin

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axis



height is 1 unit

axis


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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

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arcourt Publishin

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pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

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t Pub

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

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pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

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pany bull Im

age C

redits copy

String

erReutersC

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Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

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t Pub

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ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits

copyJasm

ina81iSto

ckPhotocom






5 ft

20 in12 in

12 in

copy H

oug

hton

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flin

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t Pub

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ng

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y




A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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oug

hton Mifflin H

arcourt Publishin

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pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

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pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


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oug

hton

Mif

flin

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cour

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


5 ft

20 in12 in

12 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




A 6 _ π

B 2 _ 3π

C 3π _ 4

D 3π _ 2



copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany



Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



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axis


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height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

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arcourt Publishin

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Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

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flin

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t Pub

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

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Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

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s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

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Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

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arcourt Publishin

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2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

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Com

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9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

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lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

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44 ft10 ft

c

b

a

lradic2

Top View

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ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

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Unit 9 1186


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Unit 9 1187


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mAth in CAreers





Unit 9 1188


copy H

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Venus 7521

Earth 7926

Mars 4222

Jupiter 88846

Saturn 74898

Uranus 31763

Neptune 30775








copy H

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y bull I

mag

e C

red

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copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

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hton

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ng

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y bull I

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e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

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10 cm 4 cm

4

6

6

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flin

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A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

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Ocean

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Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

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Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

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12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

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2 yd

3 yd10 m

5 m

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oug

hton Mifflin H

arcourt Publishin

g Com

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copy H

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flin

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768 pixels

1024 pixels

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height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

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S

S

Sh

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arcourt Publishin

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pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

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V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

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y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

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hton

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flin

Har

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Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

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pany









copy H

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flin

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

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44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

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flin

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t Pub

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ng

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y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

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t Pub

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ng

Com

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_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

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t Pub

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ng

Com

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Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

gie

n Pa

asse

nS

hutt

erst

ock









copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

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Reflect











Reflect


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10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

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redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

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pan

y











768 pixels

1024 pixels

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arcourt Publishin

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axis



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height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

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arcourt Publishin

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pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

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pan

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


copy H

oughton Mifflin H













Sun 43 times 1 0 5




0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

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Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

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pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

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t Pub

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Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

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flin

Har

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Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

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t Pub

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ng

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y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

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ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


0-2-3

-3

-2

1

2

3y

1 2 3

x

A (-2 -1) D (1 -1)

B (0 1) C (3 1)

Name Class Date

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y bull I

mag

e C

red

its

copyRe

x Fe

atur

esA

P Im

ages






P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =



P = 6 + 4 radic_

2 P =

A = 6 A =


attributes

Resource Locker

Resource Locker



6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

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flin

Har

cour

t Pub

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ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

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Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

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y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


6 ft

5 ft

12 in

3 in

8 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Reflect











Reflect


Your Turn







10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


10 cm 4 cm

4

6

6

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y






A = π (4) 2 = 16π


A = π (12) 2 = 144π




P = P =

A = A =


Reflect







12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


12

12 ft

6 ft

3 in

4 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

Ocean

C

orbis

Your Turn














r 2 + h 2 + 2π r 2


V = cu in V = cu in

S = sq in S = sq in




3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


3 in

3 in

8 in

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect





Your Turn


Elaborate





copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


12 m

21 m

24 in

9 in

6 ft

18 ft

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y









2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


2 yd

3 yd10 m

5 m

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany
















copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y











768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


768 pixels

1024 pixels

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany










axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188



axis



height is 1 unit

axis


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Name Class Date








Resource Locker





height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


height is h units

B

W

ℓ

h

S

S

Sh B

W

ℓ

h

S

S

Sh

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




Reflect




Volume of a Prism





3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


3 cm

120 ft

60 ft

8 ft

ge07se_c10l06003aAB

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y




V = ℓwh = (120) (60) (8) = 57600 f t 3


_ 0134 f t 3

to estimate


57600 f t 3 ∙ 1 gallon

_ 0134 f t 3


_ 0134 f t 3

= 1


__ 833 pounds



__ 1 gallon


__ 1 gallon

= 1





V = s 3 = = c m 3


g _

c m 3

c m 3 ∙ g _

c m 3 asymp g



Reflect





side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188



side of 2k

h

h

h

h

h

hh

h

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

Your Turn










B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


B = 81π cm2

B = 75 cm2

r = 12 inh = 45 in

4x cm5x cm

h = (x + 2) cm

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y













s 2 = c m 2

s = radic_

cm


h = 4s = 4 cm

Your Turn

Find the volume

6 7


V = Bh

= (75 c m 2 ) ( cm) = c m 3



h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


h = 22 ft

5 ft

B = 36π in2

copy H

oughton Mifflin H











V = 1000 f t 3 + 9425 f t 3 = 19425 f t 3





h = 6r = 6 ∙ = in


s = d = 2 ∙ = in


V = s 3 = 3

= i n 3








r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


r1 r2

h

r

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y

Reflect


Your Turn


Elaborate






84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


84 mm35 mm

56 mm

9 yd12 yd

15 yd

4 cm9 cm

6 cm

12 ft

10 ft

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany




2 3



6 7





14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


14 ft

12 ft

4 ft

4 ft

6 ft 10 in

15 in

5 in

6 cm

4 cm

4 cm4 cm

6 cm

6 cm6 cm 8 cm

8 cm8 cm

2 ft

2 ft

4 ft

4 ft

12 ft

17 cm

14 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany



9 10





5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


5 in

1 in

3 in

h

34 cm

60 cm

x

x + 1

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany











10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


10 cm 10 cm

10 cmFront Top Side

10 cm

4 cm 4 cm

copy H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany











2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


2 in

11 in

2 in2 in

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany









copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Substitute

Simplify


Substitute

Simplify

Find the radius

Simplify


Substitute

Simplify




V = π r 2 h

= π (3) 2 (5) = 45π c m 3



V = 1 _ 3 Bh

= 1 _ 3 (12) 2 (7)

= 336 in 3



r = 1 _ 2 (16 ft)

= 8 ft

V = 1 _ 3 π r 2 h

= 1 _ 3 π (8) 2 (18)

= 384π ft 3



V = 4 _ 3 π r 3

= 4 _ 3 π (30) 3

= 36000 π mi 3

Volume Formulas


Substitute

Simplify



95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


95

10

47

63

21

33 cm

16 cm 36 ft

4 ft

5 ft

3 m

8 m 12


1 2

3 4

5 6






copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany bull Im

age C

redits copy

String

erReutersC

orbis



Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


Ready to Go On

44 ft10 ft

c

b

a

lradic2

Top View

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y







ESSENTIAL QUESTION




11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


11 m

3 m

3 2 mradic

10 ft

3 ft2 ft

copy H

oughton Mifflin H














A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


A

C DB

40deg 40deg

A

BC

4y

0 4

x

copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

















_ π 2

m 3 True False







Unit 9 1185


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


3 cm

9 cmSALT

copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany













Unit 9 1186


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


copy H

oug

hton

Mif

flin

Har

cour

t Pub

lishi

ng

Com

pan

y








Unit 9 1187


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


copy H

oug

hton Mifflin H

arcourt Publishin

g Com

pany

mAth in CAreers





Unit 9 1188


Documents

DO NOT EDIT--Changes must be made through “File info” UNIT 9 … · 2020-03-24 · LESSON 21.1 Volume of Prisms and Cylinders LESSON 21.2 Volume of Pyramids LESSON 21.3 Volume