Answer:
54π square units.
Step-by-step explanation:
The area of a sector is given by:
[tex]A = \frac{ \theta}{360} \times \pi \: {r}^{2} [/tex]
Or
[tex]A = \frac{ \theta}{360} \times area \: of \: circle[/tex]
From the question, area of circle is 81π.
The central angle of the sector is
[tex]= 81\pi \: square \: units[/tex]
We substitute the available information to get:
[tex]A= \frac{120}{360} \times 81\pi[/tex]
[tex]A= \frac{2}{3} \times 81\pi[/tex]
This simplifies to:
[tex]A=2 \times 27\pi[/tex]
The area of the sector is
[tex]A=54\pi \: sq. \: units[/tex]
