An arc of a circle of radius 21 cm subtends an angle of 60° at the centre. Find : (i) the length of the arc. (ii) the…

Sol.
(i) Length of the arc AB = $2 \times \frac{22}{7} \times 21 \times \frac{60}{360}$
$= 22$ cm
(ii) Area of sector OALB = $\frac{22}{7} \times 21 \times 21 \times \frac{60}{360} = 231$ cm$^2$
Area of $\triangle OAB = \frac{\sqrt{3}}{4} \times 21 \times 21 = \frac{441\sqrt{3}}{4}$ cm$^2$
Area of minor segment = $\left(231 - \frac{441\sqrt{3}}{4}\right)$ cm$^2$
or $(231 - 190.95) = 40.05$ cm$^2$