Answer :
Answer:
[tex]9\pi[/tex]
Step-by-step explanation:
The area of a sector is given by;
[tex]A= \frac{1}{2} {r}^{2} \theta[/tex]
From the given information, the central angle is
[tex] \theta = \frac{ \pi}{9} [/tex]
and
[tex]A= \frac{\pi}{2} [/tex]
Let us substitute and solve for the radius, r.
[tex] \frac{ \pi}{2} = \frac{1}{2} \times {r}^{2} \times \frac{ \pi}{9} [/tex]
[tex]1 = \frac{ {r}^{2} }{9} [/tex]
[tex] {r}^{2} = 9[/tex]
[tex]r = \sqrt{9} = 3 \: units[/tex]
The area of a circle is given by:
[tex] = \pi \: {r}^{2} [/tex]
Substitute the radius to get:
[tex] = \pi \times {3}^{2} \\ = 9\pi[/tex]