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Example 1: Right Circular Cone

Find the volume of a right circular cone with height h and base of radius r

It is convenient to center the cone on the x-axis with its vertex at the origin as shown in Figure 6.2.5. This cone is the solid generated by rotating about the x-axis the triangular region R under the line y = (r/h)x, 0 ≤ x ≤ h.


Figure 6.2.5

Since x is the independent variable we use the Disc Method. The volume formula gives



V= ⅓πr2h.

Last Update: 2006-11-22