Question

the circle shown with area 9π has a sector with a central angle of 60°. what is the area of the sector? choose 1 answer a $\frac{2}{3}pi$ b $\frac{3}{2}pi$ c $\frac{1}{6}pi$ d $6pi$

Explanation:

Step1: Recall sector - area formula

The area of a sector of a circle is given by $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta$ is the central - angle of the sector and $\pi r^{2}$ is the area of the circle. Here, we know the area of the circle $A_{circle}=9\pi$ and $\theta = 60^{\circ}$.

Step2: Calculate the area of the sector

Substitute the values into the formula: $A=\frac{60^{\circ}}{360^{\circ}}\times9\pi$.
First, simplify $\frac{60}{360}=\frac{1}{6}$. Then, $A=\frac{1}{6}\times9\pi=\frac{3}{2}\pi$.

Answer:

B. $\frac{3}{2}\pi$