## Conical Frustum

A conical frustum is a Frustum created by slicing the top off a Cone (with the cut made parallel to the base). For a right circular Cone, let be the slant height and and the top and bottom Radii. Then

 (1)

The Surface Area, not including the top and bottom Circles, is
 (2)

The Volume of the frustum is given by

 (3)

But
 (4)

so
 (5)

This formula can be generalized to any Pyramid by letting be the base Areas of the top and bottom of the frustum. Then the Volume can be written as
 (6)

The weighted mean of over the frustum is
 (7)

The Centroid is then located at a height
 (8)

(Beyer 1987, p. 133). The special case of the Cone is given by taking , yielding .