Question

If an arc of a circle subtends an angle of ${60}^o$ at the centre and if the area of minor sector is $231{cm}^2$, then find the radius of the circle.

Answer 1

Area of sector $=231{cm}^2$

Angle subtended $={60}^{\circ }$

$A=\pi r^2\frac{\theta }{{360}^{\circ }}231=\frac{22}{7}\times r^2\times \frac{{60}^{\circ }}{{360}^{\circ }}\Rightarrow r^2=\frac{7}{22}\times 231\times 6=441\Rightarrow r=\sqrt{441}=21$