Respuesta :
Answer:
[tex]\text{The area of sector is }169.65 in^2[/tex]
Step-by-step explanation:
Given that the radius of circle is 18 inches and length of arc is 6π
we have to find the area of sector.
The formula to find the length of arc is
[tex]S=r\theta[/tex]
[tex]6\pi=18\times \theta[/tex]
[tex]\theta=\frac{6\pi}{18}=\frac{\pi}{3}[/tex]
Now, to find the area of sector
[tex]Area=\frac{1}{2}r^2\theta[/tex]
[tex]A=\frac{1}{2}\times 18^2\times \frac{\pi}{3}=54\pi=169.646003294\sim 169.65 in^2[/tex]
[tex]\text{Hence, the area of sector is }169.65 in^2[/tex]
Option C is correct
