What is the formula for the circumference of a circle?

The formula for the circumference of a circle is derived from the relationship between the diameter and radius of the circle. When you take the diameter (d) of the circle, which is twice the radius (r), that leads to an equivalent expression for circumference. By substituting the diameter into the formula, you can see that both expressions for circumference are valid.

The formula (C = 2\pi r) directly indicates that the circumference is proportional to the radius, with (\pi) as the constant factor. Raising the radius to any power, such as in the option involving (r^2), is not applicable in calculating circumference; instead, it pertains to area calculations. Therefore, the formula correctly relates to how the distance around the circle is constructed from its radius, making this option the accurate representation of the circumference.