Which formula is used to calculate the perimeter of a circle?

The correct formula to calculate the perimeter of a circle, which is also known as the circumference, is represented as P = 2πr. In this formula, P stands for the perimeter or circumference, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14.

This formula arises from the relationship between the diameter of a circle and its radius, where the diameter is twice the radius (d = 2r). Since the circumference of a circle is defined as the distance around it, using this relationship allows us to express that distance in terms of the radius. By substituting the diameter in terms of the radius into the formula for circumference (C = πd), we find that it simplifies to C = π(2r), which can be rewritten as C = 2πr.

Understanding this formula is crucial, as the terms for area (A = πr²) or simply the square of the radius (r²) do not apply to the measurement of the distance around a circle but rather refer to different geometric properties altogether. This distinction is key to mastering geometric calculations as related to circles.