WAEC 2013 · Paper 2 · Q4

(a)
The area of a circle is $154\text{ cm}^2$ . It is divided into three sectors such that two of the sectors are equal in size and the third sector is three times the size of the other two put together. Calculate the perimeter of the third sector. $\left[\text{Take }\pi = \frac{22}{7}\right]$

Worked solution (try it first)

Find the radius: $\frac{22}{7}r^2 = 154$ , so $r^2 = 49$ and $r = 7$ cm.
Let the two equal sectors have angle $x$ each.
The third is three times the two together: $3 \times 2x = 6x$ .
All three fill the circle: $x + x + 6x = 360^\circ$ , so $x = 45^\circ$ and the third sector's angle is $270^\circ$ .
Arc of the third sector $= \frac{270}{360} \times 2 \times \frac{22}{7} \times 7$
$= 33$ cm.
Perimeter $= 33 + 7 + 7 = 47$ cm.