Chapter 1212.7

Similar Solids

Similar Solids• Two Solids with equal ratios of

corresponding linear measurements

18

6

8

2

8

2

Ratios Not Equal Not Similar

15

10

45

30

Ratios equal

Solids are similar

Determine if the following solids are similar if so determine the scale

factor

14

7

14

7

12

5

Ratios not equal

Solids not similar

Yes: Scale Factor = 8

5

Theorem 12.13 Similar Solids Theorem

• If two solids have a scale factor of a:b then:– Corresponding area have a ratio of a2:b2

– The corresponding volumes have a ratio of a3:b3

• Example: If two similar solids have a scale factor of 4:5, then– The ratio of their surface areas is 16:25– The ratio of their volumes is 64:125

The solid is similar to a larger solid with the given scale factor. Find the surface

area S of the larger solid

Surface Area

1. surface area ratio =4

1

2

12

2832

208

4

1

inx

x

2. Set up the proportion and solve

The solid is similar to a larger solid with the given scale factor. Find the volume

V of the larger solid

Volume

1. Volume ratio =8

1

2

13

32560

320

8

1

inx

x

2. Set up the proportion and solve

The solid is similar to a larger solid with the given scale factor. Find the surface

area S of the larger solid

Surface Area

1. surface area ratio =9

1

3

12

23582

398

9

1

inx

x

2. Set up the proportion and solve

The solid is similar to a larger solid with the given scale factor. Find the volume

V of the larger solid

Volume

1. Volume ratio = 27

1

3

13

313365

495

27

1

inx

x

2. Set up the proportion and solve

The solid is similar to a larger solid with the given scale factor. Find the surface

area S of the larger solid

Surface Area

1. surface area ratio =9

4

3

22

2

4 144

9

324

x

x cm

2. Set up the proportion and solve

The solid is similar to a larger solid with the given scale factor. Find the volume

V of the larger solid

Volume

1. Volume ratio =27

8

3

23

3

8 288

27

972

x

x cm

2. Set up the proportion and solve

The solid is similar to a larger solid with the given scale factor. Find the surface

area S of the larger solid

Surface Area

1. surface area ratio =16

9

4

32

2

9 96

16512

3

x

x cm

2. Set up the proportion and solve

The solid is similar to a larger solid with the given scale factor. Find the volume

V of the larger solid

Volume

1. Volume ratio =64

27

4

33

3

27 96

642048

9

x

x cm

2. Set up the proportion and solve

Homework #69Pg 769-772 10-24 even, 25-29