WAEC 2024 · Paper 1 · Q43

Plane mensuration

The area of a sector of a circle with radius $7\text{ cm}$ is $51.3\text{ cm}^2$ . Calculate, correct to the nearest whole number, the angle of the sector. $\left[\text{Take }\pi = \frac{22}{7}\right]$

Worked solution (try it first)

Area of a sector $= \frac{\theta}{360} \times \pi r^2$ .
Here $\pi r^2 = \frac{22}{7} \times 49$
$= 154\text{ cm}^2$ .
So $\frac{\theta}{360} \times 154 = 51.3$ , and $\theta = \frac{51.3 \times 360}{154}$
$\approx 119.9^\circ$ .
To the nearest whole number, $\theta = 120^\circ$ , option B.

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