2. You are given that the centre of mass of a uniform solid cone of height \(h\) and base radius \(r\) is at a height of \(\frac { 1 } { 4 } h\) above its base. The diagram shows a solid conical frustum. It is formed by taking a uniform right circular cone, of base radius \(3 x\) and height \(6 y\), and removing a smaller cone, of base radius \(x\), with the same vertex.
\includegraphics[max width=\textwidth, alt={}, center]{d7f600c5-af4a-4708-bfd9-92b37a95c634-3_490_903_1937_575} Show that the distance of the centre of mass of the frustum from its base along the axis of symmetry is \(\frac { 18 } { 13 } y\).