Answer:
[tex]A= \frac{\pi}{2} \: square \: units[/tex]
Step-by-step explanation:
The area of a sector with the central angle
[tex] \theta[/tex]
in radian measure and radius r units is given by:
[tex]A= \frac{1}{2} {r}^{2} \theta[/tex]
We substitute
[tex] \theta = \frac{1}{9} \pi[/tex]
and r=3 to obtain:
[tex]A= \frac{1}{2} \times {3}^{2} \times \frac{1}{9} \pi[/tex]
This gives us:
[tex]A= \frac{1}{2} \times 9 \times \frac{1}{9} \pi \\ A= \frac{\pi}{2} [/tex]
