8.4 Volume and Surface Area 491 a) How many cubic yards of sand does Maya need? b) How much will the sand cost? Solution a) Since we are asked to determine the volume in cubic yards, we will convert each measurement to yards. There are 3 ft in a yard. Thus, 60 ft equals , 60 3 or 20 yd, and 30 ft equals , 30 3 or 10 yd. There are 36 in. in a yard, so 18 in. equals , 18 36 or yd. 1 2 The amount of sand needed is determined using the formula for the volume of a rectangular solid, V l w h. = ⋅ ⋅ In this case, the height of the rectangular solid can be considered the depth of the sand. V l w h 20 10 100 yd 1 2 3 = ⋅ ⋅ = ⋅ ⋅ = Note that since the measurements for length, width, and height are each in terms of yards, the answer is in terms of cubic yards. b) One cubic yard of sand costs $27, so 100 yd3 will cost 100 $27, × or $2700. 7 Now try Exercise 41 Example 3 Painting a Large Softball The Faber College Athletic Hall of Fame building features a statue of a large softball that is in need of painting. The softball has a diameter of 8.5 ft. a) Determine the surface area of the softball. b) If one quart of paint covers about 100 ft ,2 how many quarts of paint will the college need to buy to paint the softball? Solution a) The softball has the shape of a sphere with a diameter of 8.5 feet. Since the radius is half of the diameter, r 8.5 4.25. 1 2 = ⋅ = Using the formula for the surface area of a sphere: SA r 4 4 (4.25) 72.25 226.98 ft 2 2 2 π π π = = ⋅ = ≈ b) Since each quart of paint will cover about 100 ft ,2 it will take about ≈ 2.27 226.98 100 quarts of paint. Since you cannot buy a portion of a quart of paint, the college will need to buy 3 quarts of paint to paint the softball. 7 Now try Exercise 45 Example 4 Silage Storage Cletus has three silos on his farm. The silos are each in the shape of a right circular cylinder (see Fig. 8.38). One silo has a 12-ft diameter and is 40 ft tall. The second silo has a 14-ft diameter and is 50 ft tall. The third silo has an 18-ft diameter and is 60 ft tall. 12 ft 40 ft 14 ft 50 ft 18 ft 60 ft Figure 8.38 a) What is the total capacity of all three silos in cubic feet? b) If Cletus fills all three of his silos and then feeds his cattle 150 ft3 of silage per day, in how many days will all three silos be empty?
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