A piece of wire of length 24 cm is bent to form the perimeter of a sector of a circle of radius \(r\) cm.

(i) Show that the area of the sector, \(A\) cm\(^2\), is given by \(A = 12r - r^2\).

(ii) Express \(A\) in the form \(a - (r - b)^2\), where \(a\) and \(b\) are constants.

(iii) Given that \(r\) can vary, state the greatest value of \(A\) and find the corresponding angle of the sector.