Question

The area of a minor sector of a circle is 3.85 $c{m}^2$ and the measure of its central angle is ${36}^{\circ }$. Find the radius of the circle.

Answer 1

Area of minor sector of the circle $=3.85c{m}^2$

The measure of a central angle, $\theta ={36}^{\circ }$

Let the radius of the circle be $r$ cm.

Now,

Area of minor sector$=3.85c{m}^2$

$[\Rightarrow \frac{\theta }{360°}\times \pi r^2=3.85]$

$[\Rightarrow \frac{36°}{360°}\times \frac{22}{7}\times r^2=3.85]$

$[\Rightarrow r=\sqrt{\frac{3.85\times 360°\times 7}{36°\times 22}}]$

$[\Rightarrow r=\sqrt{12.25}=3.5cm]$

Thus, the radius of the circle is $3.5cm$.