The area of a sector bounded by a 180° arc with a radius of 8 miles is 32 π square miles.
The area of a sector of a circle can be calculated using the formula:
Area of sector = (central angle/360°) × π r²
The central angle is 180° and the radius r is 8 miles. Plug these values into the formula:
Area of sector = (180°/360°) × π × (8 miles)²
Simplify the expression:
Area of sector = 1/2 × π × 64 miles²
Area of sector = 32 π miles²
Therefore, the exact area of the sector bounded by a 180° arc with a radius of 8 miles is 32 π square miles.