5. (a) Use integration to show that the centre of mass of a uniform solid right circular cone of height \(h\) is \(\frac { 3 } { 4 } h\) from the vertex of the cone.
(6 marks)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ad523c3f-9109-45a8-8399-80a4c2edeff7-4_419_424_372_721}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{figure}
A paperweight is made by removing material from the top half of a solid sphere of radius \(r\) so that the remaining solid consists of a hemisphere of radius \(r\) and a cone of height \(r\) and base radius \(r\) as shown in Figure 3.
(b) Find the distance of the centre of mass of the paperweight from its vertex.
(7 marks)