Answer:
The area of the circle is equal to [tex]9\pi[/tex].
Step-by-step explanation:
Given that,
The area of sector is, [tex]\dfrac{17}{2}\pi[/tex]
The central angle is [tex]\dfrac{17}{9}\pi[/tex]
We need to find the area of circle.
We know that,
[tex]\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[/tex]
So, the area of the circle is equal to [tex]9\pi[/tex].
