How do you calculate the circumference of a circle?

The correct way to calculate the circumference of a circle is to use the formula 2πr, where r represents the radius of the circle. This formula arises from the relationship between the radius and the total distance around the circle.

The rationale behind this formula is based on the definition of π, which is the ratio of the circumference of a circle to its diameter. Since the diameter (d) is twice the radius (r), you can rearrange the formula for circumference, which can also be expressed as π times the diameter (πd). Therefore, since the diameter is 2r, you can substitute to find that the circumference can also be expressed as 2 times π times the radius.

Both 2πr and πd give you the same result, as they are simply two different ways of expressing the same calculation based on the radius and diameter respectively. This explains why the choice involving 2πr is recognized as a fundamental formula in geometry for determining the circumference of a circle.