498 CHAPTER 8 Geometry 24. 1 m 3 m 5 m 31.42 m3 25. 4 ft 3 ft 3 ft 24 ft3 26. 6 in. 8 in. 4 in. 3 in. 11 in. 132 in.3 In Exercises 27–30, use the fact that 1yd3 equals 27ft3 to make the conversion. 27. 7 yd3 to cubic feet 189 ft3 28. 15.75 yd3 to cubic feet 425.25 ft3 29. 453.6 ft3 to cubic yards 16.8 yd3 30. 278.1 ft3 to cubic yards 10.3 yd3 In Exercises 31–34, use the fact that 1 m3 equals 1,000,000 cm3 to make the conversion. 31. 1.5 m3 to cubic centimeters 1,500,000 cm3 32. 13.7 m3 to cubic centimeters 13,700,000 cm3 33. 500,000 cm3 to cubic meters 0.5 m3 34. 9,160,000 cm3 to cubic meters 9.16 m3 In Exercises 35– 40, determine the missing value indicated by the question mark. Use Euler’s Polyhedron formula. ⎛ ⎝⎜ ⎞ ⎠⎟ − ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + ⎛ ⎝⎜ ⎞ ⎠⎟ = Number of vertices number of edges number of faces 2 Number of Vertices Number of Edges Number of Faces 35. 8 12 ? 6 faces 36. 4 6 ? 4 faces 37. ? 12 8 6 vertices 38. ? 30 12 20 vertices 39. 12 ? 20 30 edges 40. 18 ? 20 36 edges In Exercises 41–56, solve the given problem. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 41. Playground Mulch Davidson is building a backyard playground for his grandchildren and wishes to put down rubber mulch to provide safety from falls. Davidson wishes to put the mulch in a pit in the shape of a rectangular solid 20 ft long, 15 ft wide, and 9 in. deep. a) Determine the volume, in cubic feet, of mulch Davidson will need. 225 ft3 b) If mulch costs $11 per cubic foot, what will the cost of the mulch be? $2475 42. Rose Garden Topsoil Marisa wishes to plant a rose garden in her backyard. The rose garden will be in the shape of a 9 ft by 18 ft rectangle. Marisa wishes to add a 4-in. layer of organic topsoil on top of the rectangular area. The topsoil sells for $42 per cubic yard. a) Determine how many cubic yards of topsoil Marisa will need. 2 yd3 b) Determine how much the topsoil will cost. $84 43. A Fish Tank a) How many cubic centimeters of water will a fish tank in the shape of a rectangular solid hold if the tank is 80 cm long, 50 cm wide, and 30 cm high? 120,000 cm3 b) If 1 cm3 holds 1 m of liquid, how many milliliters will the tank hold? 120,000 m c) If 1 1000 m , = how many liters will the tank hold? 120 44. Volume of a Freezer The dimensions of the interior of an upright freezer are height 46 in., width 25 in., and depth 25 in. Determine the volume of the freezer a) in cubic inches. 28,750 in.3 b) in cubic feet. 16.64 ft3 45. Cylindrical Tank Scott needs to paint a cylindrical tank that is used for storing diesel fuel for use on his farm. The tank has a diameter of 5 feet and a length (height) of 6 feet. The paint sells for $16.48 per quart and one $ $ $ Sergey Mironov/Shutterstock
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