WAEC 2022 · Paper 1 · Q22

Plane mensuration

In the diagram, $\angle POQ = 150^\circ$ and the radius of the circle $PSQR$ is $4.2\text{ cm}$ . Find the area of the sector $OPSQ$ . $\left[\text{Take }\pi = \frac{22}{7}\right]$

Worked solution (try it first)

Sector $OPSQ$ goes round through $S$ , away from the $150^\circ$ angle, so it is the major sector with angle $360^\circ - 150^\circ = 210^\circ$ .
Area of a sector $= \frac{\theta}{360} \times \pi r^2$ .
Here $\pi r^2 = \frac{22}{7} \times 4.2^2$
$= 55.44\text{ cm}^2$ .
So the area is $\frac{210}{360} \times 55.44 = 32.34\text{ cm}^2$ , option D.

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