What is the formula for the circumference of a circle?

The formula for the circumference of a circle is indeed given by (C = 2\pi r), where (C) represents the circumference and (r) is the radius of the circle. The constant (\pi) (pi) is approximately equal to 3.14159 and is used in calculations involving circles, as it represents the ratio of the circumference of any circle to its diameter.

This particular formula arises from the relationship between the radius and the diameter of a circle, where the diameter (d) is twice the radius, expressed as (d = 2r). Since the circumference is the distance around the circle, substituting the diameter into the relationship yields (C = \pi d), which can further be expressed as (C = \pi (2r) = 2\pi r).

In contrast, other provided options correspond to different aspects of circles. For instance, (C = \pi r^2) is the formula for the area of a circle, which measures the space contained within the circle. The option (C = 2r) incorrectly represents the relationship involving just the diameter of the circle, not the circumference. Lastly, (C = r