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

or

V= ⅓πr²h.