Answer:
[tex]169.65\text{ inch}^2[/tex]
Step-by-step explanation:
We have been given that the radius of our given circle is 18 inches and the arc length that corresponds to sector is 6 pi.
To find the area of our given sector we will use formula:
[tex]\text{Area of sector}=\pi r^2*\frac{\text{Arc length}}{\text{Circumference of circle}}[/tex]
Upon substituting our given values in above formula we will get,
[tex]\text{Area of sector}=\pi*18^2*\frac{6\pi}{2\pi*18}[/tex]
[tex]\text{Area of sector}=\pi*324*\frac{1}{6}[/tex]
[tex]\text{Area of sector}=\pi*54[/tex]
[tex]\text{Area of sector}=169.64600329\approx 169.65[/tex]
Therefore, the area of our given sector is 169.65 square inches.
