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JAMB Mathematics 2014 Paper

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Question : 47

Total: 47

If the angle of a sector of a circle with radius 10.5 cm is 120°, find the perimeter of the sector. [Take

\pi = \frac{22}{7}

]

48 cm
40 cm
43 cm
45 cm

Solution:

Concept:

The perimeter of a sector is the sum of its two radii and the arc length.

Explanation:

Formula for the perimeter of a sector:

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

Substitute

r = 10.5\text{ cm}

,

\theta = 120^\circ

,

\pi = \frac{22}{7}

:

P = 2(10.5) + \frac{120}{360} \times 2 \times \frac{22}{7} \times 10.5

Simplify:

\frac{120}{360} = \frac{1}{3}

P = 21 + \left(\frac{1}{3} \times 2 \times \frac{22}{7} \times 10.5\right)

Since

10.5 = \frac{21}{2}

,

\frac{1}{3} \times 2 \times \frac{22}{7} \times \frac{21}{2} = 22

So:

P = 21 + 22 = 43\text{ cm}

Answer:

The perimeter of the sector is

43\text{ cm}

, which is option C.

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