The cross-sectional area A of a circular pipe is proportional to the square of its diameter D. Which option correctly reflects this statement?

• A. False; A ∝ D
• B. False; A ∝ D^3
• C. True
• D. False; A is independent of D

Answer: (C)

The cross-sectional area of a circle depends on its diameter through the circle area formula. With diameter D, radius is D/2, so the area is A = π(D/2)^2 = (π/4) D^2. This shows A grows with the square of D, meaning A is proportional to D^2. Therefore, the statement is true. If the diameter doubles, the area increases by a factor of four; if it changes, the area changes accordingly with the square of the diameter. The idea that A would be proportional to D (linear) or D^3 (cubic), or independent of D, conflicts with the actual formula.