Math Is Fun Forum

Cut the frustum and inscribed sphere with a vertical plane passing through the center of the sphere and perpendicular to the two bases.

Let the slant height

and the radius of the circle

Let

since

and

, Since

. From

draw a perpendicular to base

at point

, then

is a right triangle, where

and

. Since the radius of the smaller base

we choose

  the volume of the frustum