Review question

# When is the volume of this cylinder inside a cone a maximum? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7785

## Question

A truncated cone of height $h$ has circular ends of radii $2r$ and $r$. In this cone is inserted a circular cyclinder having its axis along the axis of the cone. One end of the cylinder lies in that face of the cone which is of radius $2r$ and the circumference of the other end lies in the curved surface of the cone (see diagram). Given that the radius of the base of the cylinder is $s$, show that the volume of the cylinder is

$\frac{\pi h s^2(2r - s)}{r}.$

If $s$ is allowed to vary, find, in terms of $h$ and $r$, the maximum volume of the cylinder.