Final answer:
To find the area of a sector formed by a 180° arc in a circle with a radius of 6 feet, calculate the area of the full circle and then divide by 2. The full circle’s area is A = πr², yielding an area of 18π square feet for the sector.
Step-by-step explanation:
The question asks us to find the area of the sector bounded by a 180° arc in a circle where the radius is 6 feet. To calculate this, we need to understand that the area of a full circle is A = πr², where r is the radius of the circle. For a complete circle with a radius of 6 feet, the area would be A = π × 6² feet². Because a sector with a 180° arc is half of a complete circle, we divide the full area by 2. So, the area of the sector is A = (π × 36) / 2 or 18π square feet, which is choice (a).