WAEC 2022 · Paper 1 · Q21

Plane mensuration

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

Worked solution (try it first)

Arc length $= \frac{\theta}{360} \times 2\pi r$ .
The circumference is $2 \times \frac{22}{7} \times 4.2 = 26.4$ cm.
The minor arc is $\frac{150}{360}$ of it: $\frac{5}{12} \times 26.4 = 11$ cm, option A.

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