3.9: Sector of fixed area with minimum perimeter

0606/11/M/J/22 — Question 9 · 9 marks

A circle, centre

O

and radius

r\text{ cm}

, has a sector

OAB

of fixed area

10\text{ cm}^{2}

. Angle

AOB

\theta

radians and the perimeter of the sector is

P\text{ cm}

(a)

Find an expression for

P

in terms of

r

[3]

(b)

Find the value of

r

for which

P

has a stationary value.

[3]

(c)

Determine the nature of this stationary value.

[2]

(d)

Find the value of

\theta

at this stationary value.

[1]