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WAEC Mathematics 2024 Paper

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Question : 43

Total: 50

The area of a sector of a circle with radius 7cm is 51.3 cm

^{2}

. Calculate, correct to the nearest whole number, the angle of the sector. (Take

\pi

\frac{22}{7}

)

60 $^{0}$
120 $^{0}$
150 $^{0}$
150 $^{0}$

Solution:

Concept:

Use the formula for the area of a sector to find the unknown angle.

Explanation:

Area of a sector is given by:

A = \frac{\theta}{360} \times \pi r^2

Substitute

A = 51.3

,

r = 7

, and

\pi = \frac{22}{7}

:

51.3 = \frac{\theta}{360} \times \frac{22}{7} \times 7^2

51.3 = \frac{\theta}{360} \times \frac{22}{7} \times 49

51.3 = \frac{\theta}{360} \times 154

Now solve for

\theta

:

\theta = \frac{51.3 \times 360}{154}

\theta = \frac{18468}{154} = 119.92

To the nearest whole number,

\theta \approx 120^\circ

.

Answer:

120^\circ

(Option B).

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