3.62: Sector logo: perimeter model and minimum

0606/23/O/N/24 — Question 4 · 8 marks

3.62 diagram
The diagram shows a logo that is a sector of a circle, radius r cmr\text{ cm}, with angle α\alpha radians. The area of the logo is 9 cm29\text{ cm}^{2}.
(a)
Show that the perimeter P cmP\text{ cm} is given by P=2r+18rP = 2r + \dfrac{18}{r}.
[3]
(b)
Given that rr can vary, find the stationary value of PP and determine its nature.
[5]