Frustum of a cone The shape of the first spacecraft in the Apollo program was a frustum of...

Frustum of a cone The shape of the first spacecraft in the Apollo program was a frustum of a right circular cone—a solid formed by truncating a cone by a plane parallel to its base. For the frustum shown in the figure, the radii a and b have already been determined.

EXERCISE

(a) Use similar triangles to express y as a function of h.

(b) Derive a formula for the volume of the frustum as a function of h.

(c) If a =6 ft and b =3 ft, for what value of h is the volume of the frustum 600 ft3?