Concentric sectors: angle from a given sector area and perimeter and the exact radius of the inner sector

The diagram shows two circles with the same centre \(O\). The points \(P\) and \(Q\) lie on the outer circle, of radius \(R\) cm. The inner circle, of radius \(r\) cm, meets the radius \(OP\) at \(S\) and the radius \(OQ\) at \(T\). The angle \(P\hat{O}Q=S\hat{O}T=\theta\) radians, where \(\theta\) is acute.

The sector \(OPQ\) has an area of \(27\text{ cm}^2\) and a perimeter of \(24\text{ cm}\). The sector \(OST\) has an area of \(15\text{ cm}^2\).

1. Find \(\theta\).[5]
2. Hence find \(r\), giving your answer in exact form.[2]