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WAEC Mathematics 2011 Paper

Question : 14

Total: 47

\pi + 8

)cm. Calculate the anle of the sector

Solution:

Concept:

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

Arc length is

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

Explanation:

Given:

r = 4

cm and perimeter

= \pi + 8

Perimeter of sector

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

Substitute

r = 4

\pi + 8 = 2(4) + \frac{\theta}{360^\circ} \times 2\pi(4)

Simplify:

\pi + 8 = 8 + \frac{\theta}{360^\circ} \times 8\pi

Subtract

8

from both sides:

\pi = \frac{\theta}{360^\circ} \times 8\pi

Divide both sides by

\pi

1 = \frac{\theta}{360^\circ} \times 8

So,

8\theta = 360^\circ

\theta = \frac{360^\circ}{8} = 45^\circ

Answer:

The angle of the sector is

45^\circ

Therefore, the correct option is A. $45^\circ$ .

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