Which formula expresses the area of a circle using diameter?

• A. A=π•D²
• B. A=0.7854•R²
• C. A=0.7854•D²
• D. A=2D

Answer: (C)

To find the circle’s area using its diameter, start from the standard area formula A = πR^2 and relate the diameter to the radius with D = 2R, so R = D/2. Substitute: A = π(D/2)^2 = πD^2/4 = (π/4)D^2. Numerically, π/4 ≈ 0.7854, so A ≈ 0.7854 D^2. This shows the area is proportional to the square of the diameter with the factor 0.7854, which matches the expression that uses diameter. The other forms either use radius instead of diameter or misstate the scaling, so they don’t fit the requirement.