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WAEC Mathematics 2020 Paper

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Question : 29

Total: 48

The length of an arc of a circle of radius 3.5 cm is 1

\frac{19}{36}

cm. Calculate, correct to the nearest degree , the angle substended by the centre of the circle. [Take

\pi = \frac{22}{7}

]

55 $^{\circ}$
36 $^{\circ}$
25 $^{\circ}$
22 $^{\circ}$

Solution:

Concept:

Use the arc length formula:

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

.

Explanation:

Radius

r = 3.5 = \frac{7}{2}

cm.

Arc length

L = 1\frac{19}{36} = \frac{55}{36}

cm.

Substitute into the formula:

\frac{55}{36} = \frac{\theta}{360^{\circ}} \times 2 \times \frac{22}{7} \times \frac{7}{2}

.

Simplify the constants:

2 \times \frac{22}{7} \times \frac{7}{2} = 22

.

So,

\frac{55}{36} = \frac{22\theta}{360^{\circ}}

.

Solve for

\theta

:

\theta = \frac{55}{36} \times \frac{360^{\circ}}{22} = 25^{\circ}

.

Thus, the angle subtended at the centre of the circle is

25^{\circ}

, correct to the nearest degree.

Answer:

C.

25^{\circ}

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