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12.7 Similar Solids. By: Denana Vehab, Steven Southerland, Anisa Dokic, Edis Ramic. Vocabulary. Similar Solids- Two solids with equal ratios of corresponding linear measures, such as height or radii are called similar solids. Theorem 12.13 (Similar Solids Theorem).

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12 7 similar solids

12.7 Similar Solids

By: Denana Vehab, Steven Southerland, Anisa Dokic, Edis Ramic

vocabulary
Vocabulary
  • Similar Solids- Two solids with equal ratios of corresponding linear measures, such as height or radii are called similar solids.
theorem 12 13 similar solids theorem
Theorem 12.13 (Similar Solids Theorem)
  • If two similar solids have a scale factor of a:b then corresponding areas have a ratio of a2:b2, and corresponding volumes have a ration of a3:b3.
example 1
Example 1
  • Are the two solids similar? If so, what’s the scale factor?

4

8

Not Similar

2

3

1

6

8

4

Similar, Scale Factor = 2

2

1

4

8

example 2
Example 2
  • Find the surface area of G when the surface area of F = 24 ft2 and the ratio of the two figures is 1:3.

24 = 12

Write out the Proportion.

G = 32

24 = 1

Work out the exponents then cross multiply.

G = 9

216 ft2 = 1ft 2

Surface Area of G = 216 ft2

example 3
Example 3
  • Find the volume of Figure G when the volume of Figure F = 7 ft3 and the ration of the two figures is 1:3.

7 = 13

Write out the proportion.

G = 33

Work out the exponents then cross multiply.

7 = 1

G = 27

189 ft3 = Volume of G

The Volume of G = 189 ft3

example 4
Example 4
  • Find the Scale factor of the two cubes.

V = 512 m3

V = 1728 m3

a3 = 5123

Write out the ratio of the volumes.

b3 = 17283

a = 8

Cube root the numbers.

b = 12

2

Simplify. Once simplified, the final answer will be the scale factor.

3

assignment
Assignment
  • p. 769, #4-27 all