What is the formula for the area of a circle in terms of diameter D?

What is the formula for the area of a circle in terms of diameter D?

• A. A = π r^2
• B. A = (π/4)D^2
• C. A = π D^2/2
• D. A = 2π D

Answer: (B)

The area of a circle depends on the radius, so to use diameter you convert radius to D/2. Start from the standard formula A = πr^2 and substitute r = D/2. This gives A = π(D/2)^2 = πD^2/4, which can be written as A = (π/4)D^2. So the area in terms of diameter is A = (π/4)D^2. The other forms either use radius directly, double-count the area, or resemble a different measure (circumference), so they don’t fit the diameter expression.

The area of a circle depends on the radius, so to use diameter you convert radius to D/2. Start from the standard formula A = πr^2 and substitute r = D/2. This gives A = π(D/2)^2 = πD^2/4, which can be written as A = (π/4)D^2.

So the area in terms of diameter is A = (π/4)D^2. The other forms either use radius directly, double-count the area, or resemble a different measure (circumference), so they don’t fit the diameter expression.