# Calculus

posted by
**Grant**
.

A cone is inscribed in a sphere of radius a, centred at the origin. The

height of the cone is x and the radius of the base of the cone is r, as

shown in the diagram opposite.

Find the height, x, for which the volume of the cone is a maximum.

(HINT: show that the volume of the cone is given by

V=1/3pi(2ax^2-x^3)