Question

A circle has a sector with area 1/2 pi and central angle of 1/9 pi radians. What is the area of the circle

Answer 1

Answer:

$9\pi$ sq. units.

Step-by-step explanation:

It is given that a circle has a sector with area $\frac{1}{2}\pi$ and central angle of $\frac{1}{9}\pi$ radians.  

We know that, the area of sector is

$A=\dfrac{1}{2}r^2\theta$

where, r is radius and $\theta$ is central angle in radian.

Substitute the values of A and $\theta$.

$\dfrac{1}{2}\pi=\dfrac{1}{2}r^2(\dfrac{1}{9}\pi)$

$1=r^2(\dfrac{1}{9})$

$9=r^2$

$3=r$

The radius of the circle is 3 units.

So, the area of circle is

$A=\pi r^2$

$A=\pi (3)^2$

$A=9\pi$

Therefore, the area of circle is $9\pi$ sq. units.