1.32: Figure 2 shows the sector of a circle with centre and radius cm.

4PM1/1R/June/2024 — Question 4 · 9 marks

1.32 diagram 1
Figure 2 shows the sector OPQ\displaystyle OPQ of a circle with centre O\displaystyle O and radius r\displaystyle r cm.
OP=OQ=rcmarcPQ=(21−r)cm∠POQ=θradiansOP = OQ = r \mathrm{cm} \quad \mathrm{arc} PQ = (21 - r) \mathrm{cm} \quad \angle POQ = \theta \mathrm{radians}
The area of the sector is Acm2\displaystyle A \mathrm{cm}^2
(a) Show that A=r2(21−r)\displaystyle A = \frac{r}{2}(21 - r)
(3)
The area of the sector must be greater than or equal to 27cm2\displaystyle 27 \mathrm{cm}^2
(b) Find the set of possible values of r\displaystyle r
(4)
(c) Hence write down the set of possible values of θ\displaystyle \theta
(2)