smc

Question

An ice-cream novelty item consists of a cup in the shape of a 4-inch-tall frustum of a right circular cone, with a 2-inch-diameter base at the bottom and a 4-inch-diameter base at the top, packed solid with ice cream, together with a solid cone of ice cream of height 4 inches, whose base, at the bottom, is the top base of the frustum. What is the total volume of the ice cream, in cubic inches?

Accepted Answer

The top cone has radius 2 and height 4 so it has volume 13 (2)^2 4. The frustum is made up by taking away a small cone of radius 1, height 4 from a large cone of radius 2, height 8, so it has volume 13 (2)^2 8 - 13 (1)^2 4. Adding, we get 13 (16+32-4) = 443.