Question

The length of an arc of a circle, subtending an angle of ${54}^{\circ }$ at the centre is 16.5 cm. Calculate the radius, circumference and area of the circle.

Answer 1

Length of an arc $=\frac{\theta }{360}\times 2\pi r$

$16.5=\frac{54}{360}\times 2\times \frac{22}{7}\times r16.5=\frac{3}{20}\times 2\times \frac{22}{7}\times r16.5=\frac{3}{5}\times \frac{11}{7}\times r16.5=\frac{33}{35}\times rr=\frac{16.5\times 35}{33}=17.5$

Circumference, $C=2\pi r=2\times \frac{22}{7}\times 17.5=110cm$

Area $=\pi r^2=\frac{22}{7}\times 17.5\times 17.5=962.5c{m}^2$