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JAMB Mathematics 2016 Paper

Question : 18

Total: 50

Calculate the perimeter of a sector of a circle of raduis 12cm and angle 60o.

Solution:

Concept:

A sector's perimeter is the total distance around its boundary: two straight radii plus the curved arc length.

Explanation:

The formula for the perimeter of a sector is

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

Given: radius

r = 12\text{ cm}

and angle

\theta = 60^\circ

The two radii contribute

2r = 2(12) = 24\text{ cm}

The arc length is

\frac{60}{360} \times 2\pi(12) = \frac{1}{6} \times 24\pi = 4\pi\text{ cm}

Add both parts to get the total perimeter:

P = 24\text{ cm} + 4\pi\text{ cm} = (24 + 4\pi)\text{ cm}

Answer:

(24 + 4\pi)\text{ cm}

, which corresponds to option B.

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