Test Index

WAEC Mathematics 2025 Paper

© africaexams.com

Question : 32

Total: 50

The angle of a sector of a circle is 108 °. If the radius of the circle is 3

\frac{1}{2}

cm, find the perimeter of the sector.

6 $\frac{3}{5}$ cm
7 $\frac{2}{10}$ cm
6 $\frac{4}{5}$ cm
13 $\frac{3}{5}$ cm

Solution:

Concept:

Perimeter of a sector is the sum of the arc length and the two radii.

Explanation:

Given: angle

\theta = 108^\circ

and radius

r = 3\frac{1}{2}\text{ cm} = \frac{7}{2}\text{ cm}

.

Arc length

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

.

= \frac{108}{360} \times 2 \times \frac{22}{7} \times \frac{7}{2}

= \frac{3}{10} \times 22 = \frac{66}{10} = 6\frac{3}{5}\text{ cm}

.

Perimeter

= \text{arc length} + 2r = 6\frac{3}{5} + 2 \times \frac{7}{2} = 6\frac{3}{5} + 7 = 13\frac{3}{5}\text{ cm}

.

Answer:

13\frac{3}{5}\text{ cm}

(Option D).

© africaexams.com

Go to Question:

Prev Question

Next Question