Question

A circle has a sector with area \dfrac{17}{2}\pi 2 17 ​ πstart fraction, 17, divided by, 2, end fraction, pi and central angle of \purple{\dfrac{17}{9}\pi} 9 17 ​ πstart color #9d38bd, start fraction, 17, divided by, 9, end fraction, pi, end color #9d38bd radians . What is the area of the circle?

Answer 1

Answer:

The area of the circle is equal to $9\pi$.

Step-by-step explanation:

Given that,

The area of sector is, $\dfrac{17}{2}\pi$

The central angle is $\dfrac{17}{9}\pi$

We need to find the area of circle.

We know that,

$\text{Area of sector}=\dfrac{\text{central angle}}{2\pi}\times \text{Area of circle}\\\\\text{Area of circle}=\dfrac{2\pi \times \text{Area of sector}}{\text{central angle}}\\\\=\dfrac{2\pi \times \dfrac{17\pi}{2}}{\dfrac{17\pi }{9}}\\\\=9\pi$

So, the area of the circle is equal to $9\pi$.