Hello, hellothisismyname!

There is a right circular cone, which has been sliced to create a frustum.

The height of the entire unsliced cone is 20 inches, with 12 inches above the frustum and 8 inches below.

The other piece of information that is known is the slant height of the frustrum, which is 10 inches.

Find the radius of the original cone and the volume of the frustum.

Consider the cross-section of the cone.

We see that: .Code:A * /|\ / | \ / | \ / | \ / |12 \ / | \ / | \ D * - - - + - - - * F / E| |\ / |8 8| \10 / | | \ B * - - - - - * - - - * - * C G H

We note that is a 3-4-5 right triangle.

. . Hence:.

Since is a 3-4-5 right triangle:.

. . Hence:. . (radius of original cone)

Cone has radius and height

. . Hence:.

Cone has radius and height

. . Hence:.

Therefore:.