10.2.4 Volume of Pyramids and Cones (continued)
The volume of a cone is determined in this example. The circumference of the base is given as 18 π cm and the height of the cone is given as 12 cm. Find the length of the radius by equating the given circumference to the formula for the circumference of a circle and solve for r . The radius is 9 cm. To find the volume, substitute the radius and height into the formula for the volume of a cone. The volume is 324 π cm 3 .
Example 4 Exploring Effects of Changing Dimensions
The effect of a proportional change in dimensions on the volume of a pyramid is examined in this example. The height and base length and width are given for the pyramid. The volume of the original pyramid is calculated by substituting the given values into the formula. The base area is the length times the width of the base. The volume of the pyramid is 360 ft 3 . The new pyramid is obtained by reducing the edges of the base and the height by a factor of one-half. In the example shown, the factor of 1/2 is tracked through the calculations. The area of the new pyramid is 45 ft 3 . This value is 3 times the original volume, or one-eighth the original. The volume of the pyramid changes by the cube of the factor that was used to change the dimensions. ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1 2
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