Find the area of a sector of a circle with radius 6 cm if angle of the sector is $60^o$.

Given:

Radius of the circle $=6\ cm$.

Angle subtended by the sector $=60^o$

To do:

We have to find the area of the sector.

Solution:

Area of the sector subtending $\theta$ at the centre $=\pi r^{2} \times \frac{\theta}{360^{\circ}}$

Therefore,

Area of the given sector $=\pi(6)^{2} \times \frac{60^{\circ}}{360^{\circ}} \mathrm{cm}^{2}$

$=36 \pi \times \frac{1}{6} \mathrm{~cm}^{2}$

$=6\pi \mathrm{cm}^{2}$

The area of the sector is $6\pi \mathrm{cm}^{2}$.