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Warm-Up Exercises 1. Right rectangular prism, side lengths 8 in., 5 in., and 10 in. 2. Right cone, radius 3 m, height 4 m ANSWER 340 in. 2 ; 400 in. 3 ANSWER 75.40 m 2 ; 37.70 m 3 Find the surface area and volume of each solid.

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Warm-Up Exercises 3. Sphere, radius 7.3 ft ANSWER 669.66 ft 2 ; 1629.51 ft 3 Find the surface area and volume of each solid.

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Warm-Up Exercises EXAMPLE 1 Identify similar solids Tell whether the given right rectangular prism is similar to the right rectangular prism shown at the right. a. b.

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Warm-Up Exercises EXAMPLE 1 Identify similar solids SOLUTION The prisms are similar because the ratios of corresponding linear measures are all equal. The scale factor is 2:3. ANSWER The prisms are not similar because the ratios of corresponding linear measures are not all equal. ANSWER a. Lengths 4 8 Widths 2 4 Heights 2 2 b. Lengths 4 6 Widths 2 3 Heights 2 3 1 2 = 1 2 = 1 1 = 2 3 =

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Warm-Up Exercises GUIDED PRACTICE for Example 1 Tell whether the pair of right solids is similar. Explain your reasoning. 1. The solids are similar because the ratios of corresponding sides is in the ratio 4:3 ANSWER

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Warm-Up Exercises GUIDED PRACTICE for Example 1 Tell whether the pair of right solids is similar. Explain your reasoning. 2. The solids are similar because the ratios of corresponding sides is in the ratio 4:3 ANSWER

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Warm-Up Exercises EXAMPLE 2 Use the scale factor of similar solids Packaging The cans shown are similar with a scale factor of 87:100. Find the surface area and volume of the larger can.

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Warm-Up Exercises EXAMPLE 2 Volume of II ≈ 42.93 Surface area of II ≈ 68.49 The surface area of the larger can is about 68.49 square inches, and the volume of the larger can is about 42.93 cubic inches. ANSWER Use the scale factor of similar solids

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Warm-Up Exercises EXAMPLE 2 SOLUTION Use Theorem 12.13 to write and solve two proportions. Surface area of I Surface area of II 51.84 Surface area of II Volume of I Volume of II 28.27 Volume of II a2a2 b2b2 = = a3a3 b3b3 = 87 2 100 2 = 87 3 100 3 Use the scale factor of similar solids

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Warm-Up Exercises EXAMPLE 3 Find the scale factor The pyramids are similar. Pyramid P has a volume of 1000 cubic inches and Pyramid Q has a volume of 216 cubic inches. Find the scale factor of Pyramid P to Pyramid Q.

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Warm-Up Exercises EXAMPLE 3 Find the scale factor SOLUTION Use Theorem 12.13 to find the ratio of the two volumes. a3a3 b3b3 = 1000 216 The scale factor of Pyramid P to Pyramid Q is 5:3. ANSWER Write ratio of volumes. Find cube roots. Simplify. a b = 6 10 a b = 5 3

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Warm-Up Exercises EXAMPLE 4 Checking Solutions of a Linear Inequality A store sells balls of yarn in two different sizes. The diameter of the larger ball is twice the diameter of the smaller ball. If the balls of yarn cost $7.50 and $1.50, respectively, which ball of yarn is the better buy? Volume of large ball Volume of small ball Consumer Economics STEP 1 Compute: the ratio of volumes using the diameters. 2323 1313 = = 8 1, or 8 : 1

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Warm-Up Exercises EXAMPLE 4 Checking Solutions of a Linear Inequality Price of large ball Volume of small ball Find: the ratio of costs. =, or 5:1 5 1 STEP 2 = $ 1.50 $ 7.50

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Warm-Up Exercises EXAMPLE 4 Checking Solutions of a Linear Inequality Compare: the ratios in Steps 1 and 2. STEP 3 If the ratios were the same, neither ball would be a better buy. Comparing the smaller ball to the larger one, the price increase is less than the volume increase. So, you get more yarn for your dollar if you buy the larger ball of yarn. ANSWER The larger ball of yarn is the better buy.

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Warm-Up Exercises GUIDED PRACTICE for Examples 2, 3, and 4 Cube C has a surface area of 54 square units and Cube D has a surface area of 150 square units. Find the scale factor of C to D. Find the edge length of C, and use the scale factor to find the volume of D. 3. Volume of D =125 square units ANSWER

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Warm-Up Exercises GUIDED PRACTICE WHAT IF? In Example 4, calculate a new price for the larger ball of yarn so that neither ball would be a better buy than the other. 4. for Examples 2, 3, and 4 ANSWER $12.00

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