WAEC 2016 · Paper 2 · Q5

(a)
The diagram shows a semicircular arc on a school gate with centre $O$ and diameter $AE$ , with a shaded segment $BCD$ . If $|AE| = 14$ metres and $\angle AOB = \angle DOE = 45^\circ$ , calculate the cost of painting the shaded portion at the rate of ₦750.00 per square metre. $\left[\text{Take }\pi = \frac{22}{7}\right]$

Worked solution (try it first)

The radius is half of $AE$ : $r = 7$ m.
The angles on the diameter add up to $180^\circ$ , so $\angle BOD = 180^\circ - 45^\circ - 45^\circ$
$= 90^\circ$ .
The shaded segment $BCD$ is sector $BOD$ minus triangle $BOD$ .
Sector $= \frac{90}{360} \times \frac{22}{7} \times 7^2$
$= 38.5\text{ m}^2$ .
Triangle $= \frac12 \times 7 \times 7$
$= 24.5\text{ m}^2$ .
Segment $= 38.5 - 24.5 = 14\text{ m}^2$ .
Cost $= 14 \times ₦750 = ₦10,500$ .