An arc of a circle of radius $\displaystyle 21$ cm subtends an angle of $\displaystyle 60$° at the centre. Find :

(i)

the length of the arc.

(ii)

the area of the minor segment of the circle made by the corresponding chord.

(i) Length of the arc \(\displaystyle \mathrm{AB}=2 \times \frac{22}{7} \times 21 \times \frac{60}{360}\) \[=22 \mathrm{~cm} \]

(ii) Area of sector OALB \(\displaystyle =\frac{22}{7} \times 21 \times 21 \times \frac{60}{360}=231 \mathrm{~cm}^{2}\) \[\text { Area of } \Delta \mathrm{OAB}=\frac{\sqrt{3}}{4} \times 21 \times 21=\frac{441 \sqrt{3}}{4} \mathrm{~cm}^{2} \] \[\text { Area of minor segment }=\left(231-\frac{441 \sqrt{3}}{4}\right) \mathrm{cm}^{2} \] \[\text { or }(231-190.95)=40.05 \mathrm{~cm}^{2} \]