2019 TJC Promo Q7

A napkin-holder is formed by boring a cylindrical hole, of length \(2h\), through a wooden sphere of radius \(a\), where \(a\) is a fixed constant. The axis of the hole passes through the centre \(O\) of the sphere. The diagram shows a cross-section through \(O\), with \(x\)- and \(y\)-axes taken parallel and perpendicular to the axis of the hole respectively.

2. Let \(V\) denote the volume of the wood forming the napkin-holder. By considering the napkin-holder as a solid of revolution about the \(x\)-axis, find \(V\) in terms of \(h\), verifying that it is independent of \(a\).[4]