2
\includegraphics[max width=\textwidth, alt={}, center]{13cfb59a-7781-4786-a625-919b01a2a4f0-2_501_641_461_753} The diagram shows a circle \(C\) with centre \(O\) and radius 3 cm . The radii \(O P\) and \(O Q\) are extended to \(S\) and \(R\) respectively so that \(O R S\) is a sector of a circle with centre \(O\). Given that \(P S = 6 \mathrm {~cm}\) and that the area of the shaded region is equal to the area of circle \(C\),

1. show that angle \(P O Q = \frac { 1 } { 4 } \pi\) radians,
2. find the perimeter of the shaded region.