(i)[3]
Show that the sector area, $A\text{ cm}^2$, can be expressed as $A = 12r - r^2$.
(ii)[2]
Express $A$ in the form $a - (r - b)^2$, with $a$ and $b$ as constants.
(iii)[2]
Given that $r$ may vary, state the largest value of $A$ and find the corresponding angle of the sector.