Differentiation - Problems Involving Maximisation and Minimisation

The diagram shows a right cone with a base radius \(r\) cm and height \(h\) cm which is inscribed exactly inside a sphere of radius \(6\) cm and centre \(O\).

1. Express \(r\) in terms of \(h\).
2. The volume of cone is \(V\) cm\(^3\). Show that \(V = 4\pi h^2 - \frac{1}{3}\pi h^3\).
3. Find the value of \(r\) for which \(V\) has a turning value and determine the nature of this turning value.
4. Hence find this volume, leaving your answer in terms of \(\pi\).