What is the area of a circular roof with a 12-foot diameter?

What is the area of a circular roof with a 12-foot diameter?

• A. 113 sq ft
• B. 226 sq ft
• C. 72 sq ft
• D. 144 sq ft

Answer: (A)

Area of a circle is found with A = πr^2. With a 12-foot diameter, the radius is 6 feet, so A = π(6)^2 = 36π, which is about 113 square feet. This is the correct area for the circular roof because you’re applying the circle area formula to the actual radius. The other numbers come from common mistakes: 144 would be the diameter squared without accounting for π, 72 could come from using an incorrect π or not squaring the radius, and 226 is roughly twice the correct area, suggesting a doubling error.

Area of a circle is found with A = πr^2. With a 12-foot diameter, the radius is 6 feet, so A = π(6)^2 = 36π, which is about 113 square feet. This is the correct area for the circular roof because you’re applying the circle area formula to the actual radius. The other numbers come from common mistakes: 144 would be the diameter squared without accounting for π, 72 could come from using an incorrect π or not squaring the radius, and 226 is roughly twice the correct area, suggesting a doubling error.