The radius of the circle is half the diameter, so it is 8/2 = 4 miles.
The central angle of the sector is 180°, which is half of the full circle's central angle of 360°.
The area of the sector is given by the formula:
A = (1/2) * r^2 * θ
where r is the radius and θ is the central angle in radians.
To find θ in radians, we can use the formula:
θ (in radians) = (π/180) * θ (in degrees)
For the 180° central angle, θ in radians is:
θ = (π/180) * 180 = π
Now we can plug in the values:
A = (1/2) * 4^2 * π
A = 8π
The area of the sector is 8π square miles.