1.18: Concentric sectors and shaded annulus

The diagram shows a sector $OPQ$ of the circle centre $O$, radius $3r\text{ cm}$. The points $S$ and $R$ lie on $OP$ and $OQ$ respectively such that $ORS$ is a sector of the circle centre $O$, radius $2r\text{ cm}$. The angle $POQ = \theta$ radians. The perimeter of the shaded region $PQRS$ is $100\text{ cm}$.