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WAEC Mathematics 2022 Paper

Question : 21

Total: 47

Solution:

Concept:

The area of a sector is a fraction of the circle’s total area, based on the central angle.

Explanation:

From the diagram, the sector OPSQ has central angle

\theta = 210^\circ

and radius

r = 4.2\, \text{cm}

Use the sector area formula:

\text{Area} = \frac{\theta}{360^\circ}\pi r^2

Substitute the values:

\text{Area} = \frac{210}{360} \times \frac{22}{7} \times (4.2)^2

Simplify the fraction:

\frac{210}{360} = \frac{7}{12}

and

(4.2)^2 = 17.64

Thus,

\text{Area} = \frac{7}{12} \times \frac{22}{7} \times 17.64

Cancel the common factor

7

\text{Area} = \frac{22 \times 17.64}{12}

Calculate:

\frac{388.08}{12} = 32.34\, \text{cm}^2

Answer:

32.34\, \text{cm}^2

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