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JAMB Mathematics 2024 Paper

Question : 4

Total: 50

Find the angle subtended by an arc 33cm long of a circle of diameter 28cm.

Solution:

Concept:

The angle subtended by an arc is found using the relation between arc length, radius, and central angle.

Explanation:

Given: arc length

= 33\, \text{cm}

Diameter

= 28\, \text{cm}

, so radius

r = \frac{28}{2} = 14\, \text{cm}

Use the formula:

\text{Arc length} = \frac{\theta}{360^\circ} \times 2\pi r

Substitute

\pi = \frac{22}{7}

and

r = 14

33 = \frac{\theta}{360^\circ} \times 2 \times \frac{22}{7} \times 14

Simplify the constant:

2 \times \frac{22}{7} \times 14 = 88

33 = \frac{\theta}{360^\circ} \times 88

Multiply both sides by

360^\circ

\theta = \frac{33 \times 360^\circ}{88}

Simplify:

\theta = \frac{33 \times 360}{88} = 135^\circ

Answer:

The angle subtended is

135^\circ

, so the correct option is D.

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