Answer:
Area of circle is 9π
Step-by-step explanation:
The area of sector of a circle is given by [tex]A=\frac{1}{2}r^2\theta[/tex]
Plugging the given values in the formula, we get
[tex]\frac{1}{2}\pi=\frac{1}{2}r^2\cdot\frac{1}{9}\pi[/tex]
Cancel out 1/2 and π from both sides, we are left with
[tex]1=r^2\cdot\frac{1}{9}[/tex]
Cross multiplying, we get
[tex]r^2=9\\\\r=3[/tex]
Therefore, area of circle is given by
[tex]A=\pi r^2\\\\A=\pi(3)^2\\\\A=9\pi[/tex]
Area of circle is 9π
