Which expression gives the area of a circle with diameter 12 inches?

Which expression gives the area of a circle with diameter 12 inches?

• A. A = (3.14 x 12 x 12) ÷ 4
• B. A = πr^2
• C. A = πd^2 ÷ 2
• D. A = 2πr

Answer: (A)

The area of a circle relates to its radius, and if you know the diameter, you use half of it as the radius. Starting from A = πr^2 and substituting r = d/2 gives A = π(d/2)^2 = πd^2/4. With a diameter of 12 inches, that becomes A = π(12^2)/4 = π·144/4 = 36π square inches, which is about 113.04 in^2 when you use π ≈ 3.14. The expression that uses diameter directly to produce the area is πd^2/4, and with d = 12 it confirms the result. The other forms either require converting to a radius first (A = πr^2) or describe a different quantity (2πr is circumference), so they don’t directly give the area from the diameter.

The area of a circle relates to its radius, and if you know the diameter, you use half of it as the radius. Starting from A = πr^2 and substituting r = d/2 gives A = π(d/2)^2 = πd^2/4. With a diameter of 12 inches, that becomes A = π(12^2)/4 = π·144/4 = 36π square inches, which is about 113.04 in^2 when you use π ≈ 3.14. The expression that uses diameter directly to produce the area is πd^2/4, and with d = 12 it confirms the result. The other forms either require converting to a radius first (A = πr^2) or describe a different quantity (2πr is circumference), so they don’t directly give the area from the diameter.