Hmh alg1 mod7 1 volume of prisms & cylinders (1)

Volume of Prisms and Cylinders

Warm UpWarm UpProblem of the DayProblem of the DayLesson PresentationLesson PresentationLesson QuizzesLesson Quizzes


Warm Up

Find the area of each figure described. Use 3.14 for .

1. a triangle with a base of 6 feet and a height of 3 feet

2. a circle with radius 5 in.

9 ft2

78.5 in2


Problem of the DayYou are painting identical wooden cubes red and blue. Each cube must have 3 red faces and 3 blue faces. How many cubes can you paint that can be distinguished from one another?only 2


Learn to find the volume of prisms and cylinders.




Area is measured in square units. Volume is measured in cubic units.

Remember!


Find the volume of each figure to the nearest tenth. Use 3.14 for .

Additional Example 1A: Finding the Volume of Prisms and Cylinders

a rectangular prism with base 2 cm by 5 cm and height 3 cm

= 30 cm3

B = 2 • 5 = 10 cm2

V = Bh

= 10 • 3

Area of base

Volume of a prism


Find the volume of the figure to the nearest tenth. Use 3.14 for .

4 in.

12 in.

= 192 602.9 in3

B = (42) = 16 in2

V = Bh

= 16 • 12

Additional Example 1B: Finding the Volume of Prisms and Cylinders

Area of baseVolume of a cylinder



5 ft

7 ft

6 ft

V = Bh= 15 • 7= 105 ft3

B = • 6 • 5 = 15 ft212

Additional Example 1C: Finding the Volume of Prisms and Cylinders

Area of base

Volume of a prism



A rectangular prism with base 5 mm by 9 mm and height 6 mm.

= 270 mm3

B = 5 • 9 = 45 mm2

V = Bh

= 45 • 6

Area of base

Volume of prism

Check It Out: Example 1A



8 cm

15 cm

B = (82)= 64 cm2

= (64)(15) = 960

3,014.4 cm3

Check It Out: Example 1B

Area of base

Volume of a cylinderV = Bh



10 ft

14 ft

12 ft

= 60 ft2

= 60(14)= 840 ft3

Check It Out: Example 1C

Area of base

Volume of a prism

B = • 12 • 10 12

V = Bh


A juice box measures 3 in. by 2 in. by 4 in. Explain whether tripling the length, width, or height of the box would triple the amount of juice the box holds.

Additional Example 2A: Exploring the Effects of Changing Dimensions

The original box has a volume of 24 in3. You could triple the volume to 72 in3 by tripling any one of the dimensions. So tripling the length, width, or height would triple the amount of juice the box holds.


A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling the height of the can would have the same effect on the volume as tripling the radius.

Additional Example 2B: Exploring the Effects of Changing Dimensions

By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.


By tripling the radius, you would increase the volume nine times.

A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume.

Check It Out: Example 2

V = 36 • 3 = 108 cm3

The original cylinder has a volume of 4 • 3 = 12 cm3.

Volume of Prisms and CylindersCheck It Out: Example 2 Continued

Tripling the height would triple the volume.

V = 4 • 9 = 36 cm3

The original cylinder has a volume of 4 • 3 = 12 cm3.


A drum company advertises a snare drum that is 4 inches high and 12 inches in diameter. Estimate the volume of the drum.

Additional Example 3: Music Application

d = 12, h = 4r = = = 6

Volume of a cylinder.

d 2V = (r2)h

12 2

= (3.14)(6)2 • 4 = (3.14)(36)(4) = 452.16 ≈ 452

Use 3.14 for .

The volume of the drum is approximately 452 in3.


A drum company advertises a bass drum that is 9 inches high and 19 inches in diameter. Estimate the volume of the drum.

Check It Out: Example 3

d = 19, h = 9r = = = 9.5

Volume of a cylinder.

d 2V = (r2)h

19 2

= (3.14)(9.5)2 • 9 = (3.14)(90.25)(9) = 2550.465 ≈ 2550

Use 3.14 for .

The volume of the drum is approximately 2,550 in3.


Find the volume of the the barn.

Volume of barn

Volume of rectangular

prism

Volume of triangular

prism+=

= 30,000 + 10,000V = (40)(50)(15) + (40)(10)(50)1

2

= 40,000 ft3

The volume is 40,000 ft3.

Additional Example 4: Finding the Volume of Composite Figures

Volume of Prisms and CylindersCheck It Out: Example 4

Find the volume of the house.

3 ft

4 ft

8 ft

5 ft

= (8)(3)(4) + (5)(8)(3)12

= 96 + 60

V = 156 ft3

Volume of house

Volume of rectangular

prism

Volume of triangular

prism+=


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Volume of Prisms and CylindersLesson Quiz

Find the volume of each figure to the nearest tenth. Use 3.14 for .

306 in3942 in3 160.5 in3

No; the volume would be quadrupled because you have to use the square of the radius to find the volume.

10 in.

8.5 in.3 in.

12 in.12 in.2 in.

15 in.10.7 in.

1. 3.2.

4. Explain whether doubling the radius of the cylinder above will double the volume.


1. Identify the volume of the cylinder to the nearest tenth. Use 3.14 for .

A. 1099 in3 B. 1582.6 in3

C. 1356.5 in3 D. 1846.3 in3



2. Identify the volume of the rectangular prism to the nearest tenth.

A. 338 m3 B. 390 m3

C. 364 m3 D. 422.5 m3



3. Explain whether doubling the height of a rectangular prism will double the volume.A. Yes; the volume would be doubled because you have to use the height to find the volume. B. No; the volume would be tripled because you have to use height to find the volume.C. No; the volume would be tripled because you have to use the square of the height to find the volume.D. Yes; the volume would be doubled because you have to use the square of the height to find the volume.


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Hmh alg1 mod7 1 volume of prisms & cylinders (1)