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.

EXAMPLE 2 Use the scale factor of similar solids SOLUTION Use the Similar Solids Theorem to write and solve two proportions. Surface area of I Surface area of II a2 b2 = Volume of I Volume of II = a3 b3 51.84 Surface area of II = 872 1002 28.27 Volume of II = 873 1003

EXAMPLE 2 Use the scale factor of similar solids Surface area of II ≈ 68.49 Volume of II ≈ 42.93 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

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.

Use the Similar Solids Theorem to find the ratio of the two volumes. EXAMPLE 3 Find the scale factor SOLUTION Use the Similar Solids Theorem to find the ratio of the two volumes. a3 b3 = 1000 216 Write ratio of volumes. a b = 6 10 Find cube roots. a b = 5 3 Simplify. The scale factor of Pyramid P to Pyramid Q is 5:3. ANSWER

EXAMPLE 4 Checking Solutions of a Linear Inequality Consumer Economics 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? STEP 1 Compute the ratio of volumes using the diameters. Volume of large ball Volume of small ball 23 13 = = 8 1 , or 8 : 1

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

EXAMPLE 4 Checking Solutions of a Linear Inequality STEP 3 Compare: the ratios in Steps 1 and 2. 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.

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. Scale factor is 3 : 5; Volume of D = 125 square units Edge length is 3 units; ANSWER

Daily Homework Quiz for Examples 2, 3, and 4 Two triangular prisms are similar, with surface areas 9 ft2 and 25 ft2 . What is the scale factor of the prisms? 1. ANSWER 3 : 5 Two spheres have volumes 125π m3 and 216π m3. What is the scale factor of the spheres? What is the ratio of the surface areas? 2. ANSWER 5 : 6; 25 : 36

Daily Homework Quiz The volumes of two similar square pyramids are 8 ft3 and 27 ft3. What is the ratio of the surface area of the smaller pyramid to the larger? 3. ANSWER 4 : 9 The two solids are similar. Find the surface area and volume of Solid II. 4. ANSWER S = 361.28 cm2; V = 575.96 cm3