Which formula for circumference uses diameter?

Which formula for circumference uses diameter?

• A. c = πd
• B. c = 2πr
• C. c = d^2
• D. c = πr

Answer: (A)

The key idea is that circumference is tied to diameter through pi. Start from the standard formula C = 2πr and remember that the diameter d equals twice the radius, so r = d/2. Substituting gives C = 2π(d/2) = πd. That shows why the formula that uses diameter is C = πd: you’re multiplying the diameter by pi to get the circumference. For a quick check, if the diameter is 6, C = πd = 6π ≈ 18.85, which matches the usual C = 2πr with r = 3. The other forms either involve the radius rather than the diameter or mix in a squared term, which isn’t correct for circumference.

The key idea is that circumference is tied to diameter through pi. Start from the standard formula C = 2πr and remember that the diameter d equals twice the radius, so r = d/2. Substituting gives C = 2π(d/2) = πd. That shows why the formula that uses diameter is C = πd: you’re multiplying the diameter by pi to get the circumference. For a quick check, if the diameter is 6, C = πd = 6π ≈ 18.85, which matches the usual C = 2πr with r = 3. The other forms either involve the radius rather than the diameter or mix in a squared term, which isn’t correct for circumference.