Question

If the radius of the circle is $6cm$ and the length of an arc is $12cm$ . Find the area of the sector.

Answer 1

Given the radius of Circle $6cm$

The length of arc is given by $\frac{x}{360}\times 2\pi r$

where $x$ is angle subtended by an arc at the center of the circle

The length is $12$

so

$\frac{x}{360}\times 2\times \frac{22}{7}\times 6=12\frac{x}{360}\times \frac{22}{7}=1\cdots \left(1\right)$

The area of sector is given by

$\frac{x}{360}\times \pi r^2\frac{x}{360}\times \frac{22}{7}\times 6\times 6$

From $\left(1\right)$

$⟹1\times 6\times 6=36$

So the area of sector is $36c{m}^2$