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WAEC Mathematics 2014 Paper

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Question : 28

Total: 49

A chord subtends an angle of 120^o at the centre of a circle of radius 3.5cm. Find the perimeter of the minor sector containing the chord, [Take

\pi = \;\frac{22}{7}

]

14 $\;\frac{1}{3}$ cm
12 $\;\frac{5}{6}$ cm
8 $\;\frac{1}{7}$ cm
7 $\;\frac{1}{3}$ cm

Solution:

Concept:

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

Explanation:

For a sector with radius

r

and angle

\theta

at the centre, the perimeter is:

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

Here,

r = 3.5\,\text{cm}

and

\theta = 120^\circ

.

So, perimeter

= 2(3.5) + \frac{120}{360} \times 2 \times \frac{22}{7} \times 3.5

= 7 + \left(\frac{1}{3} \times 22\right)

= 7 + \frac{22}{3}

= \frac{21 + 22}{3} = \frac{43}{3}

= 14\frac{1}{3}\,\text{cm}

Answer:

Option A:

14\frac{1}{3}\,\text{cm}

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