9 Charles has a slice of cake; its cross-section is a sector of a circle, as shown in Fig. 9. The radius is \(r \mathrm {~cm}\) and the sector angle is \(\frac { \pi } { 6 }\) radians.
He wants to give half of the slice to Jan. He makes a cut across the sector as shown.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{aa8688bb-3608-45ab-85b7-bf84889dd189-3_420_657_497_744}
\captionsetup{labelformat=empty}
\caption{Fig. 9}
\end{figure}
Show that when they each have half the slice, \(a = r \sqrt { \frac { \pi } { 6 } }\).
Section B (36 marks)