5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c9758792-ca4c-4837-bd7c-e695fe0c0cdf-06_426_417_260_760}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The shape shown in Figure 1 is a pattern for a pendant. It consists of a sector \(O A B\) of a circle centre \(O\), of radius 6 cm , and angle \(A O B = \frac { \pi } { 3 }\). The circle \(C\), inside the sector, touches the two straight edges, \(O A\) and \(O B\), and the \(\operatorname { arc } A B\) as shown.
Find
- the area of the sector \(O A B\),
- the radius of the circle \(C\).
The region outside the circle \(C\) and inside the sector \(O A B\) is shown shaded in Figure 1.
- Find the area of the shaded region.