To solve this problem, we will use the following formula for the area of a sector:
[tex]A=\frac{\theta}{360^{\circ}}\pi r^2,[/tex]
where θ is the central angle, and r is the radius.
From the given data, we know that:
[tex]\begin{gathered} \theta=360^{\circ}-120^{\circ}=240^{\circ}, \\ r=9cm. \end{gathered}[/tex]
Therefore,
[tex]A=\frac{240^{\circ}}{360^{\circ}}\pi(9cm)^2.[/tex]
Computing the value of A, we get:
[tex]A=54\pi\text{ cm}^2.[/tex]
Answer:
[tex]\begin{equation*} 54\pi\text{ cm}^2. \end{equation*}[/tex]
