2016 TWO(e)

A cone of height $h$ and radius $r$ is inscribed, as shown, inside a sphere of radius $6$ cm.

The base of the cone is $s$ cm below the $x$-axis.

Find the value of $s$ which maximises the volume of the cone.
*You must use calculus and show any derivatives that you need to find when solving this problem.*

*You do not need to prove that the volume you have found is a maximum.*