**Question 1**:

The figure shows the sector

*OCB*of radius 13 cm at the centre*O*. The length of the arc*CB*= 5.2 cm. Find**(a)**the angle

*in radians,*

**(b)**the perimeter of the shaded region.

*Solution:***(a)**

$\begin{array}{l}s=r\theta \\ 5.2=13\left(\angle COB\right)\\ \angle COB=0.4\text{radian}\end{array}$

**(b)**

$\begin{array}{l}\mathrm{cos}\angle COB=\frac{OA}{OC}\\ \mathrm{cos}0.4=\frac{OA}{13}\text{(changecalculatortoRadmode)}\\ OA=11.97\text{cm}\\ \therefore AB=13-11.97=1.03\text{cm}\\ \\ CA=\sqrt{{13}^{2}-{11.97}^{2}}\\ CA=5.07\text{cm}\end{array}$

**Perimeter of the shaded region = 5.07 + 1.03 + 5.2 = 11.3 cm**.

**Question 2**:

The figure shows the sector

*AOB*of a circle, centre*O*and radius 5 cm. The length of the arc*AB*is 6 cm. Find the area of:**(a)**the sector

*AOB*,

**(b)**the shaded region.

*Solution:***(a)**Arc

*AB*= 6cm

*s*=

*r*θ

6 = 5 θ

θ = 6/5 rad

$\begin{array}{l}\text{Areaofsector}AOB\\ =\frac{1}{2}{r}^{2}\theta =\frac{1}{2}{\left(5\right)}^{2}\left(\frac{6}{5}\right)=15c{m}^{2}\end{array}$
**(b)**

**Question 3**:

Diagram below shows a sector

*QOR*of a circle with centre*O*.It is given that

*PS*= 8 cm and*QP*=*PO*=*OS*=*SR*= 5 cm.Find

**(a)**the length, in cm, of the arc

*QR*,

**(b)**the area, in cm

^{2}, of the shaded region.

*Solution:***(a)**Length of arc

*QR*=

*r*θ = 10 (1.75) =

**17.5 cm**

**(b)**

Area of the shaded region

= Area of sector

*QOR*– Area of triangle*POS*= ½ (10)

^{2}(1.75) – ½ (5) (5) sin 1.75 (change calculator to Rad mode)= 87.5 – 12.30

=

**75.2 cm**^{2}
Nice questions. Good revision.