Differentiation - Problems Involving Maximisation and Minimisation

The diagram shows an inverted right cone with a base radius of \(6\) cm and a height of \(18\) cm, where a cylinder with a base radius of \(r\) cm is placed upright inside the cone, such that the top of the cylinder is \(4\) cm above the top of the cone. Let the part of the cylinder inside the cone be \(h\) cm in depth.

1. Express \(h\) in terms of \(r\).
2. Find, in terms of \(r\), the volume of the cylinder.
3. Find the value of \(r\) for which the volume of the cylinder has a stationary value and determine the nature of this stationary value.