Section 10

1
Section 10 8Areas and Volumes of Similar Solids

• Objective
• To find relationships between the ratios of the
  areas and volumes of similar solids.

2
Similar Solids
Have the same shape, and all their corresponding
dimensions are proportional.
Similarity Ratio

• The ratio of corresponding LINEAR dimensions of
  two similar solids.

IMPORTANT Any two cubes or any two spheres are
similar!
3
Similar Solids
4
Example 1 Identifying Similar Solids

• A) Are the two solids similar? If so, give the
  similarity ratio.

5

• Are the two solids similar? If so, give the
  similarity ratio.
• B) C)

6
Relationships of side lengths, surface areas, and
volumes of similar figures
7
Theorem 10 12 Areas and Volumes of Similar
Solids
 
8
Example 2 Finding Volume of a Sphere

•  

9

•  

10

•  

 
11
Example 3 Using A Similarity Ratio

•  

12

•  

13

•  

14

•  

15
Homework

• Textbook Page 568 569 1- 16 All

16
(No Transcript)
17
Section 10 8Continued
Objective To find relationships between the
ratios of the areas and volumes of similar solids.
18
Example 4 Real-World Connection

• A) A marble paperweight shaped like a pyramid
  weighs 0.15 lb. How much does a similarly shaped
  marble paperweight weight if each dimension is
  three times as large?

19

• B) A box of detergent shaped like a rectangular
  prism is 6 in. high and holds 3.25 lb of
  detergent. How much detergent would a similar
  box that is 8 in. high hold? Round your answer to
  the nearest tenth.

20

• C) A solid chocolate rabbit is 6 in. high and
  weighs 0.25 lb. A similar chocolate rabbit is 12
  in. high. How much does it weigh?