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WAEC Mathematics 2016 Paper

Question : 36

Total: 49

\pi = \frac{22}{7}

]

Solution:

Concept:

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

Explanation:

For a sector of radius

r

and angle

\theta

, the perimeter is given by:

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

Here,

r = 21\,\text{cm}

and perimeter

= 64\,\text{cm}

, with

\pi = \frac{22}{7}

Substitute the values:

64 = 2(21) + \frac{\theta}{360^\circ} \times 2 \times \frac{22}{7} \times 21

64 = 42 + \frac{\theta}{360^\circ} \times 132

Subtract

42

from both sides:

22 = \frac{\theta}{360^\circ} \times 132

22 = \frac{132\theta}{360^\circ}

Simplify

\frac{132}{360}

\frac{11}{30}

22 = \frac{11\theta}{30}

Multiply both sides by

30

and divide by

11

\theta = \frac{22 \times 30}{11} = 60^\circ

Thus, the angle of the sector is

60^\circ

Answer:

60^\circ

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