Answer:
[tex]8\pi\text{ mi}^2[/tex]
Step-by-step explanation:
The area of a full circle is [tex]A = \pi r^2[/tex] where r is the radius.
The area of the circle in this problem is [tex]A=\pi(8)^2=64\pi[/tex].
A 45 degree central angle (that's how arcs are measured) accounts for 1/8 of the circle (because it's 45 degrees out of a full circle of 360 degrees, and 45/360 = 1/8).
The area of the sector is [tex]\frac{1}{8}(64\pi)=8\pi[/tex] square miles
