490 CHAPTER 8 Geometry In Example 1(b), the volume of the cylinder is about 2309.07in..3 In Example 1(c), the volume of the cone with the same radius and height as the cylinder is about 769.69in. .3 Notice that the volume of the cylinder is about three times the volume of the cone, which is what we expect. Example 1 Volume and Surface Area Determine the volume and surface area of each of the following three-dimensional figures. When appropriate, use the π key on your calculator and round your answer to the nearest hundredths. 11 mm 5 mm 23 mm (a) (b) (d) (c) 9 cm 15 in. 7 in. 15 in. 7 in. Solution a) V lwh 23 5 11 1265 mm3 = = ⋅ ⋅ = SA lw wh lh 2 2 2 2235 2511 22311 230 110 506 846 mm2 = + + = ⋅ ⋅ + ⋅ ⋅ + ⋅ ⋅ = + + = b) V r h 7 15 735 2309.07 in. 2 2 3 π π π = = ⋅ ⋅ = ≈ SA rh r 2 2 2 7 15 2 7 2 2 π π π π = + = ⋅ ⋅ ⋅ + ⋅ ⋅ 210 98 308 967.61 in.2 π π π = + = ≈ c) V r h 1 3 1 3 7 15 1 3 49 15 245 769.69 in. 2 2 3 π π π π = = ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ = ≈ SA r r r h 7 7 7 15 2 2 2 2 2 2 π π π π = + + = ⋅ + ⋅ ⋅ + 49 7 49 225 π π = ⋅ + ⋅ ⋅ + 49 7 274517.96in.2 π π = + ≈ d) V r 4 3 4 3 9 4 3 729 972 3053.63 cm 3 3 3 π π π π = = ⋅ ⋅ = ⋅ ⋅ = ≈ SA r 4 4 9 4 81 324 1017.88 cm 2 2 2 π π π π = = ⋅ ⋅ = ⋅ ⋅ = ≈ 7 Now try Exercise 11 Example 2 Replacing a Sand Volleyball Court Maya needs to replace the sand in her rectangular sand volleyball court. The court is 60 ft long by 30 ft wide, and the sand has a uniform depth of 18 in. (see the following figure). Sand sells for $27 per cubic yard. 18 in. 60 ft 30 ft Fabio formaggio/123RF
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