Question

Find the area and perimeter of a sector with a central angle of ${60}^{\circ }$ in a circle of radius $7cm$.

Answer 1

Given: Radius of a circle $=7cm$

Cetral angle, $\theta ={60}^{\circ }$

Area of a sector with central angle ${60}^{\circ }=\frac{\theta }{{360}^{\circ }}\times \pi \times r^2$

$=\frac{{60}^{\circ }}{{360}^{\circ }}\times \pi \times 7^2$

$=\frac{1}{6}\times \frac{22}{7}\times 7\times 7$

$=\frac{11\times 7}{3}=25.67c{m}^2$

Perimeter of sector $=$ Length of the corresponding arc $+2\times$ Radius $=L+2r$

so, length of arc with ${60}^{\circ }$ central angle, $L=\frac{{60}^{\circ }}{{360}^{\circ }}\times 2\times \pi \times r$

$=\frac{1}{6}\times 2\times \frac{22}{7}\times 7$

$=\frac{22}{3}=7.33cm$

Perimeter of sector $=L+2r$
$=7.33+2\times 7$
$=7.33+14=21.33cm$