Which expression represents the circumference of a circle in terms of diameter?

Which expression represents the circumference of a circle in terms of diameter?

• A. πd
• B. 2πr
• C. πr^2
• D. d^2

Answer: (A)

The circumference of a circle is proportional to its diameter, with the constant of proportionality being pi. This means you can express circumference directly in terms of diameter as C = πd. That direct relationship is why using πd is the correct way to write circumference when you’re given the diameter. You can see why it’s equivalent to the radius form as well: since the diameter is twice the radius, d = 2r, so C = πd = π(2r) = 2πr. That shows the two common formulas are the same circle, just written with different measurements. The other expressions don’t match the task. πr^2 is the area of a circle, not circumference. d^2 isn’t a standard circumference formula and doesn’t relate to pi in a way that gives correct units or value. 2πr is correct for circumference, but it uses the radius, not the diameter.

The circumference of a circle is proportional to its diameter, with the constant of proportionality being pi. This means you can express circumference directly in terms of diameter as C = πd. That direct relationship is why using πd is the correct way to write circumference when you’re given the diameter.

You can see why it’s equivalent to the radius form as well: since the diameter is twice the radius, d = 2r, so C = πd = π(2r) = 2πr. That shows the two common formulas are the same circle, just written with different measurements.

The other expressions don’t match the task. πr^2 is the area of a circle, not circumference. d^2 isn’t a standard circumference formula and doesn’t relate to pi in a way that gives correct units or value. 2πr is correct for circumference, but it uses the radius, not the diameter.