It is required to find the area of the sector AOB in terms of π.
Notice that the central angle is 120º.
Recall that the Area of a sector is given as:
[tex]A=\frac{\theta}{360^{\circ}}\times\pi r^2[/tex]
Where θ is the central angle and r is the radius.
Substitute θ=120º and r=9 into the formula:
[tex]\begin{gathered} A=\frac{120^{\circ}}{360^{\circ}}\times\pi(9^2) \\ \end{gathered}[/tex]
Evaluate the expression on the right:
[tex]A=\frac{\cancel{120^{\circ}}1}{\cancel{360^{\circ}}3}\times81\pi=\frac{1}{3}\times81\pi=27\pi\text{ square units}[/tex]
Hence, the required area of the sector in terms of π is 27π.
