Answer:
[tex]A=\frac{1}{2}[/tex]
Step-by-step explanation:
The area of sector of a circle (in radians) is:
[tex]A=\frac{1}{2}r^2 \theta[/tex]
Where
r is the radius
[tex]\theta[/tex] is the angle of the sector
We know the angle but we need the radius.
We are given the total circle's area is [tex]9\pi[/tex], putting in area of circle formula, we find the radius:
[tex]\pi r^2=9\pi\\r^2=9\\r=3[/tex]
Now, using the values, we find the area of the sector:
[tex]A=\frac{1}{2}r^2 \theta\\A=\frac{1}{2}(3)^2 (\frac{1}{9})\\A=\frac{1}{2}*9*(\frac{1}{9})\\A=\frac{1}{2}[/tex]
Area of sector is [tex]\frac{1}{2}[/tex]
