What is the formula for the circumference of a circle?

The formula for the circumference of a circle is represented accurately by the expression 2πr, where r stands for the radius of the circle. This equation indicates that the circumference is directly proportional to the radius; as the radius increases, the circumference also increases. The constant π (pi), approximately equal to 3.14159, serves as the scaling factor that relates the radius of the circle to its circumference, demonstrating the essential geometric relationship between these dimensions.

Additionally, another common formulation for the circumference is πd, where d represents the diameter of the circle. Since the diameter is twice the radius (d = 2r), both formulas describe the same relationship. However, the prominence of the expression that includes the radius in this context emphasizes the fundamental nature of the radius in defining circular geometry.

Overall, the correct choice captures the essential relationship needed to calculate the circumference of a circle, making it a fundamental formula in geometry.