In the diagram \(AOB\) and \(DOC\) are sectors of a circle centre \(O\). The angle \(AOB\) is \(x\) radians. The length of the arc \(AB\) is \(40\text{ cm}\) and the radius \(OB\) is \(16\text{ cm}\).

(i) Find the value of \(x\).

(ii) Find the area of sector \(AOB\).

(iii) Given that the area of the shaded region \(ABCD\) is \(140\text{ cm}^2\), find the length of \(OC\).