How is the circumference of a circle calculated?

The circumference of a circle is calculated using the formula (C = 2\pi r), where (C) represents the circumference and (r) is the radius of the circle. This formula derives from the relationship between the diameter and the radius; the diameter is twice the radius ((d = 2r)). Since the circumference is directly proportional to the diameter, it can also be expressed as (C = \pi d). However, using the radius in the formula is often more convenient for calculations, especially when the radius is a known quantity.

This option reflects the fundamental geometric relationship that a circle's circumference is a product of the radius and the mathematical constant (\pi). Understanding this formula is crucial for solving various problems involving circles in both basic geometry and more advanced applications, such as in physics or engineering contexts.

In summary, the formulation (C = 2\pi r) is a direct and clear way to determine the circumference based on the circle's radius, making it the correct choice for calculating the circumference of a circle.