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

The formula to calculate the circumference of a circle is expressed as C = 2πr, where C represents the circumference, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159. This formula derives from the relationship that the circumference is directly proportional to the radius; specifically, it states that the circumference is twice the product of pi and the radius.

By using this formula, one can easily determine how far it is around a circle simply by knowing its radius. For example, if the radius of the circle is 3 units, applying the formula gives C = 2 * π * 3, resulting in a circumference of approximately 18.85 units.

The formula C = πd, which is also related to the circumference, uses the diameter of the circle (d) instead of the radius, with the relationship between diameter and radius being that d = 2r. Hence, this alternative formula can also calculate the circumference but typically requires knowledge of the diameter rather than the more commonly used radius.

The option that states C = πr² is actually the formula for the area of a circle, not the circumference. The area calculates the space contained within the circle, while