What is the formula for calculating the circumference of a circle?

The formula for calculating the circumference of a circle is given by Circumference = 2πr, where r is the radius of the circle. This relationship arises from the definition of pi (π), which is the ratio of the circumference of any circle to its diameter. Since the diameter (d) is twice the radius (d = 2r), substituting this into the formula Circumference = πd leads to the same expression as Circumference = 2πr.

Using this formula, you can calculate the circumference by simply multiplying the radius by 2π. This gives you a direct way to find the distance around the circle based on its size. The use of pi is essential in these calculations as it provides the constant ratio that is true for all circles, making this formula universally applicable.

The other options do not represent the correct relationship for circumference. For example, Circumference = πr² is actually the formula for the area of a circle, not its circumference. Similarly, the expression r² / π does not correspond to any standard geometric formula related to circles. Understanding the correct formula is fundamental in geometry and helps in accurately determining the properties of circles.