The diagram shows a sector \(POQ\) of a circle, centre \(O\), radius \(r\text{ cm}\), where angle \(POQ=\theta\) radians. The perimeter of the sector is \(20\text{ cm}\).

(i) Show that the area, \(A\text{ cm}^2\), of the sector is given by \(A=10r-r^2\).

It is given that \(r\) can vary and that \(A\) has a maximum value.

(ii) Find the value of \(\theta\) for which \(A\) has a maximum value.