Question

Question 5 (ii)
In a circle of radius 21 cm, an arc subtends an angle of ${60}^{\circ }$ at the centre. Find:
(ii) area of the sector formed by the arc

Answer 1

(ii) Angle subtend by the arc = ${60}^{\circ }$

Area of the sector making angle $\theta$
$=\left(\frac{\theta }{{360}^{\circ }}\right)\times \pi r^2$

Area of the sector making angle ${60}^{\circ }$
$=\left(\frac{{60}^{\circ }}{{360}^{\circ }}\right)\times \pi r^{2}c{m}^2$ $=\left(\frac{1}{6}\right)\times {21}^2\pi =\frac{441}{6}\pi c{m}^2$ $=\frac{441}{6}\times \frac{22}{7}c{m}^2=231c{m}^2$

$\therefore$ Area of the sector formed by the arc is $231c{m}^2$