Question

In a circle of radius $21cm$, an arc subtends an angle of ${60}^{\circ }$ at the centre.

Find :

(i) the length of the arc

(ii) area of the sector formed by the arc.

Answer 1

It is given that, radius $=21cm$.

The Arc subtends an angle of ${60}^{\circ }$

(i) length $\left(l\right)$ of the arc is given by

$\Rightarrow l=\frac{\theta }{{360}^{\circ }}\times 2\pi r$

Where $r=21cm$ and $\theta ={60}^{\circ }$

$\Rightarrow l=\frac{{60}^{\circ }}{{360}^{\circ }}\times 2\times \frac{22}{7}\times 21cm$

$\Rightarrow l=22cm$

$\therefore$ Length of the arc $=22cm$.

(ii) Area of the sector formed by the arc is given by
$A=\frac{\theta }{{360}^{\circ }}\times \pi r^2$

Where $r=21cm$ and $\theta ={60}^{\circ }$

$\Rightarrow A=\frac{{60}^{\circ }}{{360}^{\circ }}\times \frac{22}{7}\times 21\times 21c{m}^2$

$\Rightarrow A=231c{m}^2$

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