What is the formula for the circumference of a circle?

The formula for the circumference of a circle can be derived from the relationship between the diameter and the radius of the circle. The circumference, which is the distance around the circle, is calculated by the formula C = 2πr, where r represents the radius.

In this formula, the factor of 2 accounts for the fact that the diameter (which is twice the radius) is being used in the calculation. Thus, the circumference can also be expressed in terms of the diameter as C = πd, since the diameter (d) is equal to 2r, making both forms of the formula valid. However, when specifically asking for the circumference based on the radius, C = 2πr is the most direct and commonly used representation.

The other choices listed do not represent the correct formula for circumference. For instance, C = πr² is the formula for the area of a circle, and C = 2r does not include the scale factor of π that is essential for calculating circumference. This is why C = 2πr is the correct and widely accepted formula for determining the circumference of a circle.