LESSON 11.1 I can identify and name 3- dimensional figures I can identify and name parts of 3-D...

LESSON 11.1

• I can identify and name 3-dimensional figures

• I can identify and name parts of 3-D figures (faces, bases, edges, vertices)

• I can identify the shape of cross sections of 3-D figures and find the area of the cross sections

solidflat surfaces

polygons

2parallelcongruent

2parallel congruent

1 basepoint

vertex

shape base(s)

Rectangular prism Pentagonal pyramid

Triangular prism Trapezoidal prism

Pentagonal prism Square (or rectangular) pyramid

∆ABC , ABED, BEFC,ADFC∆DEF

AB BC CA DE EF FD BE CF ADA, B, C, D, E, F

parallel basescircles

circularbase vertex

plane

circle rectangle

rectangle rectangle

44

4

square

A = bh

A = 4(4)

A = 16 un2

Isosceles triangle

A = ½ bh

A = ½ 18(12)

A = 108 cm2

triangle

A = ½ bh

A = ½ 9(6)

A = 27 un2

rectangle

A = bh

A = 10(6)

A = 60 in2

11-1 worksheet

ASSIGNMENT

LESSON 11-2

I can draw 2-d models for 3-d figures

I can surface area using nets

2 pattern

Top

Bottom

Front

Back

Left

Right

1

26

88

10

SA = square + 4 triangles

= 64 + 4 (40)

= 224 un2

7

3

5

3

55

35

SA = 6 rectangles

21

35

21

15 15

= 142 un2

7

15

48π

SA = rectangle + 2 circles

15(8π)120π + 2π(42)

+ 32π= 152π

≈ 477.52 cm2

Shape of

Lateral Faces

Number of

Lateral Faces

Number of

Bases

Shape of

Base

& Number of Sides

Number of Edges

Number of Vertices

Ex Octagonal Prism 8 2 8 24 16

1 Square

Prism 4 2 4 12 8

2 Rectangular Prism 4 2 4 12 8

3 Pentagonal

Prism 5 2 5 15 10

4 Triangular

Prism 3 2 3 9 6

Draw pictures!

Use the solids to answer the questions for each shape.

Investigation #1 - Prisms

Number of

curved surfaces

Shape of

Curved surface when

flattened

Number of

Bases

Shape of

Base

Number of curved edges

Number of apexes

(like a vertex)

8 Cylinder 1 2 2 none

9 Cone 1 1 1 1

10 Sphere 1 none none none none

11 Hemisphere 1 1 1 none

Draw pictures!

Use the solids and the nets to answer the questions for each shape.

Investigation #3 – Solids Involving Circles

Shape of

Lateral Faces

Number of

Lateral Faces

Number of

Bases

Shape of

Base

& Number of Sides

Number of Edges

Number of Vertices

Ex Pentagonal Pyramid 5 1 5 10 6

5Square

Pyramid 4 1 4 8 5

6 Octagonal

Pyramid 8 1 8 16 9

7 Triangular Pyramid 3 1 3 6 4

Draw pictures!

Use the solids to answer the questions for each shape.

Investigation #2 - Pyramids

Prisms PyramidsLateral Faces Rectangles Triangles

Bases Two matching polygons

One polygon

Edges Base edges times 3 Base edges times 2

Vertices Base vertices times 2 Base vertices +1

Name ____________ prism __________ pyramid

When the base is a circle it’s called a…

Cylinder Cone

11.1 Identify parts of 3d figuresSummarize the differences between prisms and pyramids

(name of base) (name of base)

1. Draw and label a net for the following solid. Then find the surface area.

Warm Up

8 888 8

3

3

3

3

3

3

22

22

2 2

16 1624 24

6

6

SA = 16+16+24+24+6+6 = 92 un2

11-2 worksheet

ASSIGNMENT

LESSON 11-3

I can find the volume of prisms

I can find the volumes of cylinders

V = Bh

B = area of base

V = πr2h

= π(82)

= 1120π mm3

≈ 3518.58 mm3

(17.5)

V = πr2h

= π(82)

= 1920π cm3

≈ 6031.86 cm3

(30)

V = πr2h

= π(62)

= 414π in3

≈ 1300.62 in3

(11.5)

V = πr2h

= π(3.52)

= 294π ft3

≈ 923.63 ft3

(24)

V = πr2h

24 ft

B = 1/2h(b1+b2)

= 1/2(1.5)(2 + 4)

= 4.5

V = Bh

= 4.5 (6)

= 27 cm3

B = 1/2Pa

= 1/2(36)(5.2)

= 93.6

V = Bh

= 93.6 (12)

= 1123.2 in3

B = bh

= 10(15)

= 150

V = Bh

= 150

= 1800 ft3

(12)

B = 1/2bh

= 1/2(9)(6)

= 27

V = Bh

= 27(10)

= 270 un3

V = Bh

735 = 42h42 42

17.5 cm = h

V = Bh

196 = 16B

16 16

16 = B

?

?164 in by 4 in

11-3 worksheet

ASSIGNMENT

LESSON 11-4

I can find the volume of pyramids

I can find the volume of cones

segmentvertex

base

heightlateral face

segmentvertex

perpendicularbase

V = 1/3 Bh

B = area of base

V = 1/3 πr2h

V = 1/3 πr2h

= 1/3 π(42)(7)

= 37.3π in3

≈ 117.29 in3

V = 1/3 πr2h

= 1/3 π(102)(24)

= 800π ft3

≈ 2513.27 ft3

24

V = 1/3 πr2h

= 1/3 π(62)(8)

= 96π cm3

≈ 301.59 cm3

8

r = 10

h = 12.73

V = 1/3 πr2h

= 1/3 π(102)(12.73)

= 424.3π yd3

≈ 1333.08 yd3

B = bh

= 8(8)

= 64

V = 1/3 Bh

= 1/3 (64)

= 21.33 ft3

(10)

8

B = 1/2bh

= 1/2(6)(8)

= 24

V = 1/3 Bh

= 1/3 (24)

= 120 ft3

(15)

4

3

B = bh

= 8(6)

= 48

V = 1/3 Bh

= 1/3 (48)

= 48 yd3

(3)

5

1010

B = bh

= 10(10)

= 100

V = 1/3 Bh

= 1/3 (100)

= 400 cm3

(12)

V = 1/3 πr2h

96π =1/3 πr2(8) π π96 = 1/3 r2(8) (3) (3)

288 = r2(8) 8 8

36 = r2

6 = r

V = 1/3 πr2h

2500π =1/3 π 52(h) π π2500 = 1/3 (25)(h) (3) (3)

7500 = 25h 25 25

300 = h

11-4 worksheet

ASSIGNMENT

LESSON 11-5

I can find surface area of spheres

I can find volume of spheres

V =4πr3

3

SA = 4πr2

V =2πr3

3

SA = 4πr2

= 4π(6)2

= 144π cm2

≈ 452.39 cm2

V =4πr3

3

=4π(6)3

3

= 288π cm3

≈ 904.78 cm3

SA = 4π(4)2

= 64π cm2 ≈ 201.06 cm2

V =4π(4)3

3

= 85.3π cm3

≈ 268.08 cm3

V =2πr3

3

=2π(16)3

3

= 2730.7π m3

≈ 8578.64 m3

V =2π(10)3

3

= 666.6π in3

≈ 2094.44 in 3

C = πd58 = πd

18.46 = d9.23 = r

SA = 4π(9.23)2

≈ 1070.57 m2

9.23 = r

V =4π(9.23)3

3

≈ 3293.77 cm3

V =4πr3

3

288π =4πr3

3

216 = r3

6 = r

SA = 4π(6)2

= 144π cm2

SA = 4πr2

324π = 4πr2

81 = r2

9 = r

V =4π(9)3

3

= 972π in3

11-5 worksheet

ASSIGNMENT

LESSON 11-6

I can find the volume of composite figures

cone + cylinder4

cone:V = 1/3 πr2h

= 1/3 π(3)24

= 12π

cylinder:V = πr2h

= π(3)25.1

= 45.9π

Total : 57.9π ≈ 181.9 cm3

rectangular prism

V = Bh

= 2100 (10)

= 21000

triangular prism

V = Bh

= 120 (70)

= 8400

Total = 29,400 ft3

11-6 worksheet

ASSIGNMENT

LESSON 11-7

I can identify properties of similar solids

I can find volume and surface area of similar solids

shapesize

a : b

a2 : b2

a3 : b3

congruent similar

1 : 3

similar

2 : 1

neither

1 : 2

12 : 22 or 1 : 4

13 : 23 or 1 : 8

8 : 5

82 : 52 or 64 : 25

83 : 53 or 512 :125

12 : 15

4

5

4 : 5

=10

x12.5 m

42 : 52 or 16 : 25 16

25=

280x 437.5 m2

43 : 53 or 64 :125 64

125=

400x 781.25 m3

8 : 6

4

3

4 : 3

=11

x8.25 cm

42 : 32 or 16 : 916

9=

x325 577.78 cm2

43 : 33 or 64 :27 64

27=

1345x 567.42 cm3

11-6 worksheet

ASSIGNMENT