Question

If the area of a sector of a circle which subtends an angle of ${60}^{\circ }$ at the centre is $\frac{77}{3}c{m}^2$, then the radius of the circle is ..............cm.

Answer 1

Given,

Angle subtended by the sector $\theta ={60}^{\circ }$

Area of the sector$=\frac{77}{3}c{m}^2$

Let, the radius be $r$

so,

$\frac{\theta }{360}\times \pi r^2=\frac{77}{3}$

$\Rightarrow \frac{60}{360}\times \frac{22}{7}\times r^2=\frac{77}{3}$

$\Rightarrow \frac{1}{6}\times \frac{22}{7}\times r^2=\frac{77}{3}$

$\Rightarrow r^2=\frac{77\times 6\times 7}{3\times 22}$

$\Rightarrow r^2=49$

$\Rightarrow r=7$

Hence, the radius of the circle is $7cm$.