12.7 Similar Solids

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12.7 Similar Solids

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

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Vocabulary

• Similar Solids- Two solids with equal ratios of
  corresponding linear measures, such as height or
  radii are called similar solids.

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Theorem 12.13 (Similar Solids Theorem)

• If two similar solids have a scale factor of ab
  then corresponding areas have a ratio of a2b2,
  and corresponding volumes have a ration of a3b3.

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Example 1

• Are the two solids similar? If so, whats the
  scale factor?

4
8
Not Similar
2
3
1
6
8
4
Similar, Scale Factor 2
2
1
4
8
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Example 2

• Find the surface area of G when the surface area
  of F 24 ft2 and the ratio of the two figures is
  13.

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
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Example 3

• Find the volume of Figure G when the volume of
  Figure F 7 ft3 and the ration of the two
  figures is 13.

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
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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.
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Assignment

• p. 769, 4-27 all