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EXAMPLE 2

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. Packaging. Surface area of I. Volume of I. =. =. Surface area of II. Volume of II. 87 3. 87 2. =. =. 100 3. 100 2.

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EXAMPLE 2

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  1. 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 Packaging

  2. Surface area of I Volume of I = = Surface area of II Volume of II 873 872 = = 1003 1002 28.27 51.84 a3 a2 Volume of II Surface area of II b3 b2 EXAMPLE 2 Use the scale factor of similar solids SOLUTION Use Theorem 12.13 to write and solve two proportions.

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

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

  5. 10 6 1000 a a = b b 216 5 = 3 a3 = b3 The scale factor of Pyramid P to Pyramid Q is 5:3. ANSWER EXAMPLE 3 Find the scale factor SOLUTION Use Theorem 12.13 to find the ratio of the two volumes. Write ratio of volumes. Find cube roots. Simplify.

  6. 8 1 23 13 Volume of large ball , or 8 : 1 Volume of small ball = = 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.

  7. $ 7.50 $ 1.50 5 1 Price of large ball Volume of small ball = , or 5:1 = EXAMPLE 4 Checking Solutions of a Linear Inequality STEP 2 Find: the ratio of costs.

  8. ANSWER The larger ball of yarn is the better buy. 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.

  9. 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. a a b b 3 5 a2 54 = b2 150 3 5 = = for Examples 2, 3, and 4 GUIDED PRACTICE Use Theorem 12.13 to find the ratio of the two properties. SOLUTION Write ratio of volumes. Find square roots. Simplify.

  10. C edge D edge 3 = 5 D edge = 5 Volume of D = 125 square units for Examples 2, 3, and 4 GUIDED PRACTICE Find the edge length. Surface area = 54 square units Single side = 9 units Edge length = 3 units Find volume of D Use Scale Factor.

  11. 4. 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. price of small ball Volume ratio of large ball 8 1.50 = 12.00 $12.00 ANSWER for Examples 2, 3, and 4 GUIDED PRACTICE SOLUTION Find the value of the volume ratio of large ball and price of small ball

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