Which relation correctly connects cross-sectional area A to diameter D for a circular pipe?

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

Answer: (D)

The relationship starts from the circle area formula in terms of diameter. The cross-sectional area of a circular pipe with diameter D is A = π (D/2)^2, which simplifies to A = (π/4) D^2. To connect A back to D, solve for D: D^2 = 4A/π, so D = sqrt(4A/π). This is the correct connection because it directly derives from the circle area formula. The other forms miss the factor of 4 or ignore the geometric link altogether, so they don’t match how area and diameter relate for a circle.