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WAEC Mathematics 2017 Paper

Question : 13

Total: 49

\pi = \frac{22}{7}

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Solution:

Concept:

Use the arc length formula to relate the arc length, radius, and the central angle in degrees.

Explanation:

The formula for the length of an arc is:

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

Here,

L = 7.5\text{ cm}

r = 7.5\text{ cm}

, and

\pi = \frac{22}{7}

Substitute the known values into the formula:

7.5 = \frac{\theta}{360^\circ} \times 2 \times \frac{22}{7} \times 7.5

Simplify the right-hand side:

7.5 = \frac{\theta}{360^\circ} \times \frac{330}{7}

Multiply both sides by

360^\circ \times \frac{7}{330}

\theta = \frac{7.5 \times 360^\circ \times 7}{330}

\theta = \frac{18900^\circ}{330}

\theta = 57.27^\circ

Correct to the nearest degree,

\theta = 57^\circ

Answer:

57^{\circ}

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