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

The formula for calculating the circumference of a circle is derived from the relationship between the diameter and the radius of the circle. The circumference, which is the distance around the circle, can be represented in two equivalent forms.

Firstly, using the radius, the circumference can be expressed as ( C = 2\pi r ), where ( r ) is the radius of the circle. This equation shows that for every unit of radius, the circumference increases by ( 2\pi ). This formula is fundamental in geometry and is widely used in various applications involving circles.

Alternatively, circumference can also be calculated using the diameter of the circle, which is twice the radius. This leads to another representation: ( C = \pi d ), where ( d ) is the diameter. Since ( d = 2r ), both formulations ultimately convey the same relationship.

The other formulas provided do not represent the circumference correctly. The formula ( C = \pi r^2 ) actually calculates the area of a circle, not its circumference. The formula ( C = 2r ) omits the essential factor of ( \pi ), which is crucial for circular measurements, and thus does not provide the correct circumference. Therefore, the