The diagram shows a circle with centre \(O\) and radius \(r\) cm. The minor arc \(AB\) is such that angle \(AOB\) is \(\theta\) radians. The area of the minor sector \(AOB\) is \(48\text{ cm}^2\).

(i) Show that \(\theta=\dfrac{96}{r^2}\).

(ii) Given that the minor arc \(AB\) has length \(12\) cm, find the value of \(r\) and of \(\theta\).

(iii) Using your values of \(r\) and \(\theta\), find the area of the shaded region.