Ok, we know that 120° is 1/3 of 360° that is the angle total of the circunference, so the of a sector bounded by a 120° will be 1/3 of the total area.
So, we are going to use the next equation:
[tex]\text{Area}=\frac{1}{3}\pi r^2[/tex]
So, replacing the radius we get:
[tex]=\frac{1}{3}(3)^2\pi[/tex][tex]=\frac{1}{3}(9)\pi[/tex][tex]=\frac{9}{3}\pi[/tex][tex]=3\pi[/tex]
Now, we are going to convert square kilometers to square miles:
[tex]=3\pi km^2\cdot\frac{1mile^2}{2.59km^2}[/tex][tex]\cong3.64miles^2[/tex]
The area of a sector bounded by a 120° arc is aproximately 3.64 square miles.
