Which formula gives the circumference of a circle in terms of the radius?

Which formula gives the circumference of a circle in terms of the radius?

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

Answer: (D)

The circumference can be expressed in terms of the radius by using the relationship between diameter and radius. Start with the familiar formula for circumference in terms of diameter: c = πd. Since diameter is twice the radius (d = 2r), substitute to get c = π(2r) = 2πr. So the circumference equals 2π times the radius. This matches the correct form c = 2πr. The other expressions aren’t in terms of the radius: c = πd uses diameter; c = πr^2 is the area formula; c = 2d would give a result that doesn’t match the actual circumference.

The circumference can be expressed in terms of the radius by using the relationship between diameter and radius. Start with the familiar formula for circumference in terms of diameter: c = πd. Since diameter is twice the radius (d = 2r), substitute to get c = π(2r) = 2πr. So the circumference equals 2π times the radius.

This matches the correct form c = 2πr. The other expressions aren’t in terms of the radius: c = πd uses diameter; c = πr^2 is the area formula; c = 2d would give a result that doesn’t match the actual circumference.