5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e500e20b-9060-4c69-af13-fb97b9a86dfd-09_529_713_223_612}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows the region \(R\) bounded by part of the curve with equation \(y = \cos x\), the \(x\)-axis and the \(y\)-axis. A uniform solid \(S\) is formed by rotating \(R\) through \(2 \pi\) radians about the \(x\)-axis.
- Show that the volume of \(S\) is \(\frac { \pi ^ { 2 } } { 4 }\)
- Find, using algebraic integration, the \(x\) coordinate of the centre of mass of \(S\).