8.4 Volume and Surface Area 499 quart covers 100 square feet. Only whole quarts may be purchased. a) Determine the surface area of the tank. 133.52 ft2 b) How many quarts of paint does Scott need to purchase? 2 qt c) What is the cost of the paint? $32.96 46. Conical Tank Troy needs to paint a conical tank that is used for storing rainwater that runs off his house’s rooftop. The tank has a diameter of 4 feet and a height of 8 feet. The paint sells for $27.38 per pint and one pint covers 50 square feet. Only whole pints may be purchased. a) Determine the surface area of the tank. 64.38 ft2 b) How many pints of paint does Troy need to purchase? 2 pt c) What is the cost of the paint? $54.76 47. Baseball Display Case A baseball is displayed in a cubeshaped glass case. The diameter of the baseball and the length of each side of the cube are both 7.5 cm. What is the volume of the air outside the baseball that is inside the closed case? 200.98 cm3 48. Softball Display Case A softball is displayed in a cube-shaped glass case. See Exercise 47 for a similar description involving a baseball. The diameter of the softball and the length of each side of the cube are both 3.8 inches. What is the volume of the air outside the softball that is inside the closed cube? 26.14 in.3 49. WNBA Basketball A regulation WNBA basketball has a diameter of 9.15 inches. a) Determine the volume of air inside the basketball. 401.11 in.3 b) Determine the surface area of the basketball. 263.02 in.2 50. NBA Basketball A regulation NBA basketball has a diameter of 9.47 inches. a) Determine the volume of air inside the basketball. 444.68 in.3 b) Determine the surface area of the basketball. 281.74 in.2 $ Tiero/123RF 51. Comparing Cake Pans When baking a cake, you can choose between a circular pan with a 9-in. diameter and a 7 in. 9 in. × rectangular pan. a) Determine the area of the base of each pan. Circular pan base: 63.62 in. ;2 rectangular pan base: 63 in.2 b) If both pans are 2 in. deep, determine the volume of each pan. Circular pan volume: 127.23 in. ;3 rectangular pan volume: 126 in.3 c) Which pan has the larger volume? Circular pan 52. Ice-Cream Comparison The Louisburg Creamery packages its homemade ice cream in tubs and in boxes. The tubs are in the shape of a right cylinder with a radius of 3 in. and height of 5 in. The boxes are in the shape of a cube with each side measuring 5 in. Determine the volume of each container. Tubs: 141.37 in. ;3 boxes: 125 in.3 53. Tent Volume The Kalittas’ tent is in the shape of a triangular prism. As seen in the following diagram, the triangle has a base of 6 feet and a height of 5 feet. The tent is 12 feet long. a) Determine the volume of the tent in cubic feet. 180 ft3 b) One cubic yard is equal to 27 cubic feet. Determine the volume of the tent in cubic yards. 6.67 yd3 5 ft 12 ft 6 ft 5 ft 54. Attic Space The attic above Raven’s garage is in the shape of a triangular prism (see Exercise 53 for a diagram of a different triangular prism). The triangle has a base of 32 feet and a height of 6 feet. The attic is 21 feet long. a) Determine the volume of the attic in cubic feet. 2016 ft3 b) Determine the volume of the attic in cubic yards. 74.67 yd3 55. Cake Icing A bag used to apply icing to a cake is in the shape of a cone with a diameter of 3 in. and a height of 6 in. How much icing will this bag hold when full? 14.14 in.3 56. Pool Toys A Wacky Noodle Pool Toy, frequently referred to as a “noodle,” is a cylindrical flotation device made from cell foam. One style of noodle is a cylinder that has a diameter of 2.5 in. and a length of 5.5 ft. Determine the volume of this style of noodle in a) cubic inches. 323.98 in . 3 b) cubic feet. 0.19 ft3
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