WAEC Mathematics 2019 Paper

Concept:The angle subtended by an arc at the centre is twice the angle subtended at the circumference. Use the arc length formula to find $ZY$.Explanation:Given: $\angle ZXY = 70^\circ$ at the circumference of the circle.This angle subtends the same arc $ZY$ as the central angle $\angle ZOY$.So, $\angle ZOY = 2 \times \angle ZXY$$\angle ZOY = 2 \times 70^\circ = 140^\circ$.The radius of the circle is $r = 18$ cm and $\pi = \frac{22}{7}$.Length of arc $ZY$ is given by:$L = \frac{\theta}{360^\circ} \times 2 \pi r$Substitute $\theta = 140^\circ$, $r = 18$ cm and $\pi = \frac{22}{7}$:$L = \frac{140^\circ}{360^\circ} \times 2 \times \frac{22}{7} \times 18$Simplify: $\frac{140}{360} = \frac{7}{18}$$L = \frac{7}{18} \times 2 \times \frac{22}{7} \times 18 = 44$ cm.Answer:The length of arc $ZY$ is $44$ cm.Correct option: C. $44$ cm.