12.7 Similar Solids

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

Theorem (Similar Solids Theorem)  If two similar solids have a scale factor of a:b then corresponding areas have a ratio of a 2 :b 2, and corresponding volumes have a ration of a 3 :b 3.

Example 1  Are the two solids similar? If so, what’s the scale factor? Not Similar Similar, Scale Factor = 2

Example 2  Find the surface area of G when the surface area of F = 24 ft 2 and the ratio of the two figures is 1:3. 24 = 1 2 G = 3 2 Write out the Proportion. Work out the exponents then cross multiply. 216 ft 2 = 1ft 2 Surface Area of G = 216 ft 2 24 = 1 G = 9

Example 3  Find the volume of Figure G when the volume of Figure F = 7 ft and the ration of the two figures is 1:3.  Find the volume of Figure G when the volume of Figure F = 7 ft 3 and the ration of the two figures is 1:3. 7 = 1 G = 27 Write out the proportion. Work out the exponents then cross multiply. 189 ft 3 = Volume of GThe Volume of G = 189 ft 3 7 = 1 3 G = 3 3

Example 4  Find the Scale factor of the two cubes. V = 512 m 3 V = 1728 m 3 a = 8 b = 12 Write out the ratio of the volumes. Cube root the numbers. a 3 = b 3 = Simplify. Once simplified, the final answer will be the scale factor.