10-810-8Areas and Volumes of Areas and Volumes of

Similar SolidsSimilar SolidsTheorem 10-12Theorem 10-12Similar SolidsSimilar Solids

Similarity RatioSimilarity Ratio

VocabularyVocabulary Similar SolidsSimilar Solids

Similarity RatioSimilarity Ratio

If similar solids If similar solids have the same have the same shape, all of their shape, all of their corresponding corresponding shapes are shapes are proportional.proportional.

The ratio of The ratio of corresponding corresponding linear dimensions of linear dimensions of two similar solids.two similar solids.

#1 Identifying Similar Solids

Are the two cylinders similar? If so, give the similarity ratio.

1210

6

5

65

1210

LargeSmall

6 : 565

65

Theorem 10-12

Areas and Volumes of Similar Solids If the similarity ratio of two similar solids is a:b,

then1. the ratio of their corresponding areas is

a2:b2, and

2. the ratio of their volumes is a3:b3

#2 Finding the Similarity Ratio

Find the similarity ratio of two similar prisms with surface areas 144 m2 and 324 m2.

324144

2

2

ba

ba

ba

2

2

3 : 2324144

ba

1812

ba

#3 Using a Similarity Ratio The volume of two similar solids are 128 m3 and 250

m3. The surface area of the larger solid is 250 m2. What is the surface area of the smaller solid?

250128

2

1 VV

3

3

12564

ba

2

2

2

1

54

SS

2516

2501 S

400025 1 S

21 m 160S

22

12564

54

2516

#4 Using a Similarity Ratio The volume of two similar solids are 5 m3 and 40 m3.

The surface area of the smaller solid is 4 m2. What is the surface area of the larger solid?

405

2

1 VV

3

3

405

ba

23

23

2

1

)40()5(

SS

70.1192.24

2

S

80.4692.2 2 S

22 m 16S

70.1192.2

#5 Using a Similarity Ratio Two similar square pyramids have volumes of 48 cm3

and 162 cm3. The surface area of the larger pyramid is 135 cm2. Find the surface area of the smaller pyramid.

16248

2

1 VV

3

3

278

ba

2

2

2

1

32

SS

94

1351 S

5409 1 S2

1 cm 60S

66

278

32

94

#6 Using a Similarity Ratio Two similar square pyramids have surface areas of 52

cm2 and 208 cm2. The volume of the larger pyramid is 192 cm3. Find the volume of the smaller pyramid.

20852

2

1 SS

164

ba

3

3

2

1

21

VV

81

1921 V

1928 1 V3

1 cm 24V

1313

164

21

42

81

Assignment

Page 568-569 #1-16