10.2.4 Volume of Pyramids and Cones (continued)
The volume of a trapezoidal pyramid is determined in this example. The lengths of the bases, the height of the base, and the height of the pyramid are given. Calculate the area of the base of the pyramid using the formula for the area of a trapezoid. The area is 26 cm 2 . Substitute the area of the base and the given pyramid height into the formula for the volume of a pyramid. The volume of the pyramid is 260/3 ≈ 86.7 cm 3 .
Example 2 Architecture Application
The volume of a pyramid is estimated in cubic feet and cubic yards in this application example. The area of the base of the pyramid and the height of the pyramid are given. Substitute the area of the base and the height into the formula for the volume of a pyramid. The volume of the pyramid is 38,400,000 ft 3 . To find the volume in cubic yards, divide the volume of cubic feet by 3 3 = 27, the number of cubic feet in a cubic yard. The volume is about 1,422,222 yd 3 .
Example 3 Finding Volumes of Cones
The volume of a cone is determined in this example. The radius of the base and the height of the cone is given. To find the volume, substitute the given values into the formula for the volume of a cone. The volume is 80 π cm 3 .
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