Definition/Procedure Example 4.4 Volume and Surface Area The volume of a three-dimensional object is a measure of the amount of space occupied by the object or the amount of space inside the object. Volume is measured in cubic units, the number of cubic units it takes to fi ll the object. (p. 319) 4 in. 3 in. 1 in. If we say that the volume of this box is 12 in3, it means that we can fi t twelve 1-in3 boxes inside this larger box. Volume of a Rectangular Solid A rectangular solid is a box-like shape with dimensions of length, width, and height. The volume, V, of a rectangular solid (or box) with length l, width w, and height h is Volume length width height or V lwh A cube is a rectangular solid in which all sides are the same length. The volume of a cube with side length s is Volume s s s or V s3 (p. 319) Find the volume of this box. 6 m 2 m 1 5 2 m 3 4 V lwh V 6 m a2 3 4 mb a2 1 5 mb Substitute the values. V 6 m a 11 4 mb a 11 5 mb Change to improper fractions. V 363 10 m3 or 36 3 10 m3 Multiply. We can express our answer in either of these ways. Volume of a Rectangular Pyramid The volume, V, of a rectangular pyramid with height h, and a base of length l and width w is Volume 1 3 length width height or V 1 3 lwh Because lw equals the area of the base, we can also think of the volume formula as V 1 3 Ah, where A lw, the area of the base of the pyramid. (p. 321) Find the volume of the pyramid with the given dimensions. 3 yd 2 yd 1 yd V 1 3 lwh V 1 3 (3 yd)(1 yd)(2 yd) Substitute the values. V 2 yd3 Multiply. www.mhhe.com/messersmith CHAPTER 4 Summary 347
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