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

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

Explanation:

Given that,

The area of sector is,
`(17)/(2)\pi`

The central angle is
`(17)/(9)\pi`

We need to find the area of circle.

We know that,

`\text{Area of sector}=\frac{\text{central angle}}{2\pi}* \text{Area of circle}\\\\\text{Area of circle}=\frac{2\pi * \text{Area of sector}}{\text{central angle}}\\\\=(2\pi * (17\pi)/(2))/((17\pi )/(9))\\\\=9\pi`

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