WAEC 2020 · Paper 1 · Q31

Plane mensuration

The length of an arc of a circle of radius $3.5\text{ cm}$ is $1\frac{19}{36}\text{ cm}$ . Calculate, correct to the nearest degree, the angle subtended at the centre of the circle. $\left[\text{Take }\pi = \frac{22}{7}\right]$

Worked solution (try it first)

Write the arc as an improper fraction: $1\frac{19}{36} = \frac{55}{36}$ cm.
The circumference is $2 \times \frac{22}{7} \times 3.5 = 22$ cm.
The angle is the arc's share of $360^\circ$ : $\theta = \frac{55}{36} \div 22 \times 360$ .
$\frac{55}{36} \times 360 = 550$ , and $550 \div 22 = 25$ .
So $\theta = 25^\circ$ , option C.

Report a problem with this question