GEOMETRY HELP Are the two solids similar? If so, give the similarity ratio. Both solid figures have the same shape. Check that the ratios of the corresponding dimensions are equal. The ratio of the radii is, and the ratio of the height is The cones are not similar because = / Quick Check Areas and Volumes of Similar Solids LESSON 11-7 Additional Examples

GEOMETRY HELP Find the similarity ratio of two similar cylinders with surface areas of 98 ft 2 and 2 ft 2. Use the ratio of the surface areas to find the similarity ratio. = Simplify a2b2a2b2 = Take the square root of each side abab The similarity ratio is 7 : 1. = The ratio of the surface areas is a 2 : b 2. a2b2a2b Areas and Volumes of Similar Solids LESSON 11-7 Additional Examples Quick Check

GEOMETRY HELP Two similar square pyramids have volumes of 48 cm 3 and 162 cm 3. The surface area of the larger pyramid is 135 cm 2. Find the surface area of the smaller pyramid. Step 1: Use the ratio of the volumes to find the similarity ratio. = Take the cube root of each side abab = The ratio of the volumes is a 3 : b 3. a3b3a3b = Simplify. a3b3a3b Areas and Volumes of Similar Solids LESSON 11-7 Additional Examples

GEOMETRY HELP Step 2: Use the similarity ratio to find the surface area S 1 of the smaller pyramid. S1S2S1S2 = Simplify S = Substitute 135 for S 2, the surface area of the larger pyramid S 1 = 135 Solve for S S 1 = 60Simplify. The surface area of the smaller pyramid is 60 cm 2. (continued) = The ratio of the surface areas is a 2 : b 2. S1S2S1S Areas and Volumes of Similar Solids LESSON 11-7 Additional Examples Quick Check

GEOMETRY HELP 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. tall hold? Round your answer to the nearest tenth. The ratio of the heights of the boxes is 6 : 8, so the similarity ratio is 6 : 8, or 3 : 4 in simplest terms. Because the weights are proportional to the volumes, the ratio of the weights equals the cube of their similarity ratio: 3 3 : 4 3, or 27 : 64. Areas and Volumes of Similar Solids LESSON 11-7 Additional Examples

GEOMETRY HELP = Let x  the weight of the larger box of detergent x x = 64  3.25 Cross-Product Property. 27x = 208 Simplify. x Divide each side by 27. The box that is 8 in. tall would hold about 7.7 lb of detergent. (continued) Areas and Volumes of Similar Solids LESSON 11-7 Additional Examples Quick Check