What is the formula for the circumference of a circle?

The formula for the circumference of a circle is given by 2πR, where R represents the radius of the circle. This formula derives from the geometric definition of a circle. The circumference is the distance around the circle, and π (pi) is a constant approximately equal to 3.14159 that represents the ratio of the circumference of any circle to its diameter.

To understand this better, when we refer to the radius, we are looking at the distance from the center of the circle to any point on its perimeter. Since the diameter is twice the radius (D = 2R), substituting 2R into the circumference formula reveals its dependence on the radius. Thus, the factor of 2πR efficiently encapsulates how the circumference scales with changes in the radius.

Other options are not correct because they do not represent the relationship needed to calculate the distance around the circle. For example, πR² is the formula for the area of the circle, while R² + π does not have any geometric significance in relation to circumference. Likewise, 4πR does not reflect the correct relationship and suggests an incorrect scale for circumference relative to radius.