Question

The radius of a circle is 8 miles. What is the area of a sector bounded by a 180° arc?Give the exact answer in simplest form. ____ square miles.

Answer 1

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.

Answer 2

Radius r:

r = 8 miles

Area of a circle:

A = π * r²

The area of a 180° arc is the half of the area of the entire circle:

A_arc = (π * r²)/2

Solving:

A_arc = 32π square miles