What is the formula to calculate the circumference of a circle?

The formula to calculate the circumference of a circle is expressed as 2πr, where r represents the radius of the circle. This formula derives from the definition of the circumference, which is the distance around a circle.

To understand this further, consider the relationship between the diameter and the radius of a circle. The diameter, which is twice the radius (d = 2r), directly links the circumference to both the radius and the diameter. By substituting the expression for diameter into the circumference formula, we can also express the circumference as πd.

Using the radius in the formula is particularly useful because it is often easier to measure. Thus, 2πr effectively communicates that the circumference is a linear measurement that increases proportionally with the radius.

So, in summary, the option indicating 2πr correctly captures the relationship between the radius of the circle and the total distance around it, making it the right choice for calculating the circumference.