8.4 Volume and Surface Area 495 Another special category of polyhedra is the pyramid. Unlike prisms, pyramids have only one base. The figures illustrated in Fig. 8.43 are pyramids. Note that all but one face of a pyramid intersect at a common vertex. (d) (c) (b) (a) Pyramids Figure 8.43 If a pyramid is drawn inside a prism, as shown in Fig. 8.44, the volume of the pyramid is less than that of the prism. In fact, the volume of the pyramid is one-third the volume of the prism. s h Volume of square prism 4 3 48 in . Volume of remaining solid 480 37.70 36 48 358.30 in. 2 2 3 3 = ⋅ = ⋅ = ≈ − − − ≈ Thus, the volume of the remaining solid is about 358.30 in. .3 7 Now try Exercise 15 Figure 8.44 Volume of a Pyramid = V Bh 1 3 where B is the area of the base and h is the height. Example 8 Volume of a Pyramid Determine the volume of the pyramid shown in Fig. 8.45. Solution First determine the area of the base, B, of the pyramid. Since the base of the pyramid is a square, s Area of base 5 25 m 2 2 2 = = = Now use this information to determine the volume of the pyramid. V B h 25 6 50m 1 3 1 3 3 = ⋅ ⋅ = ⋅ ⋅ = Thus, the volume of the pyramid is 50 m .3 7 Now try Exercise 17 6 m 5 m 5 m Figure 8.45 Cubic Unit Conversions In certain situations, converting volume from one cubic unit to a different cubic unit might be necessary. For example, when purchasing topsoil you might have to change the amount of topsoil from cubic feet to cubic yards prior to placing your order. Example 9 shows how that may be done.
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