The surface area, SA, of a three-dimensional object is the total area on the surface of the object. Therefore, surface area is measured in square units. We can fi nd the surface area of a rectangular solid with length l, width w, and height h using the formula SA 2lw 2lh 2wh. A container used to ship cargo overseas by ship has the given measurements. Find the volume and surface area of the container. 8 ft 1 2 8 ft Solution Let’s fi nd the volume fi rst. We will use the formula V lwh. Identify the length, width, and height. l 20 ft w 8 ft h 8 1 2 ft V lwh V (20 ft)(8 ft) a8 1 2 ftb Substitute the values. V (20 ft)(8 ft) a 17 2 20 ft ftb Change to an improper fraction. 4 ft) a V (20 ft)(8 17 21 ftb Divide out 2. V 1360 ft3 Multiply. The container will hold 1360 ft3 of cargo. To fi nd the surface area, use the formula SA 2lw 2lh 2wh. SA 2lw 2lh 2wh SA 2(20 ft)(8 ft) 2(20 ft) a8 1 2 ftb 2(8 ft) a8 1 2 ftb Substitute the values. SA 2(20 ft)(8 ft) 2(20 ft) a 17 2 ftb 2(8 ft) a 17 2 ftb Change the mixed numbers to improper fractions. SA 320 ft2 340 ft2 136 ft2 Multiply. SA 796 ft2 Add. The surface area of the container is 796 ft2. Notice that volume is measured in cubic feet while surface area is measured in square feet. EXAMPLE 2 YOU TRY 2 American Airlines regulations state that the dimensions of the largest allowable carry-on baggage are 22 in. long, 14 in. wide, and 9 in. tall. Find the volume and surface area of a suitcase with those dimensions. (www.aa.com) 328 CHAPTER 4 Basic Geometry Concepts and Algebra www.mhhe.com/messersmith
messersmith_power_prealgebra_1e_ch4_7_10
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