Question

The circle with centre O' has a radius of 4. If the area of the shaded region is 14 $\pi$ , then what is the value of x?

Answer 1

Given the area of shaded region is $14\pi$ and radius of circle is 4

Then area of circle =$\pi r^2=\pi (4{)}^2=16\pi$

Then Area of unshaded portion = $16\pi -14\pi =2\pi$

We know that $A_s=\frac{\theta }{360}\times \pi r^2$

Where $A_s$ is area of arc ans $\theta$ the angle of arc

$\Rightarrow 2\pi =\frac{\theta }{360}\times 16\pi$

$\Rightarrow \theta ={45}^0$

Then x=180-90-45=45