1.17: Sector area as a function of radius

0606/13/O/N/18 — Question 2 · 6 marks

1.17 diagram
The diagram shows a sector POQPOQ of a circle, centre OO, radius r cmr\text{ cm}, where angle POQ=θPOQ = \theta radians. The perimeter of the sector is 20 cm20\text{ cm}.
(i)
Show that the area, A cm2A\text{ cm}^2, of the sector is given by A=10r−r2A = 10r - r^{2}.
[3]
(ii)
It is given that rr can vary and that AA has a maximum value. Find the value of θ\theta for which AA has a maximum value.
[3]