2024 TMJC P1 Q2

A cylinder with height \(h\) cm and base radius \(r\) cm is inscribed within a sphere with fixed radius \(k\) cm. The circumference of the circular top and bottom of the cylinder is in contact with the sphere (see figure above). By using differentiation, find, in terms of \(k\), the exact value of \(h\) for which the volume of the cylinder is maximum.[6]