Question

In an arc of a circle subtends an angle of 45${}^o$ at the centre and if the area of minor sector is 77 cm${}^2$, then find the radius of the circle (in cm).

Answer 1

Given:

Area of minor sector, $A=77c{m}^2$

Angle subtended by sector, $\theta ={45}^o$

To find: Radius $r$

Area of minor sector subtending angle of ${\theta }^o$ at center of a circle of radius $r$ is given by $A=\frac{\theta }{360}\times \pi r^2$

Substituting values, we get:

$77=\frac{45}{360}\times \pi r^2$

$r\approx \sqrt{\frac{77\times 360}{45\times 22/7}}\because \pi \approx 22/7$

$r=14cm$