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JAMB Mathematics 2016 Paper

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Question : 28

Total: 50

An arc subtends an angle of 30º at the centre of a circle radius 12cm. Calculate the length of the arc.

6 $\pi$ cm
2 $\pi$ cm
3 $\pi$ cm
9 $\pi$ cm

Solution:

Concept:

Arc length is a fraction of the circumference of the circle, determined by the central angle.

Explanation:

Use the formula for arc length:

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

.

Here,

\theta = 30^\circ

and

r = 12

cm.

Substitute the values:

L = \frac{30}{360} \times 2\pi \times 12

.

Simplify:

\frac{30}{360} = \frac{1}{12}

.

Then,

L = \frac{1}{12} \times 24\pi = 2\pi

cm.

Answer:

The length of the arc is

2\pi

cm.

Correct option: B.

2\pi

cm.

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