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12.7 Similar Solids

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

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  1. 12.7 Similar Solids By: Denana Vehab, Steven Southerland, Anisa Dokic, Edis Ramic

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

  3. 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.

  4. 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

  5. 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

  6. 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

  7. 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

  8. Assignment • p. 769, #4-27 all

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