Which expression gives the circumference in terms of the circle's diameter?

Which expression gives the circumference in terms of the circle's diameter?

• A. πd
• B. 2πr
• C. πr^2
• D. πd^2

Answer: (A)

The circumference scales directly with the diameter: C = πd. This comes from the standard formula C = 2πr and the fact that the diameter d is twice the radius (d = 2r). Substituting r = d/2 into C = 2πr gives C = 2π(d/2) = πd. So the expression that gives circumference in terms of the diameter is πd. The other forms don’t match circumference: πr^2 is area, 2πr uses radius, and πd^2 is not a valid circumference expression.

The circumference scales directly with the diameter: C = πd. This comes from the standard formula C = 2πr and the fact that the diameter d is twice the radius (d = 2r). Substituting r = d/2 into C = 2πr gives C = 2π(d/2) = πd. So the expression that gives circumference in terms of the diameter is πd. The other forms don’t match circumference: πr^2 is area, 2πr uses radius, and πd^2 is not a valid circumference expression.