How is the circumference of a circle calculated?

The circumference of a circle is defined as the total distance around the circle. It can be calculated using the formula ( C = 2\pi r ), where ( C ) represents the circumference and ( r ) is the radius of the circle. The reason this formula works is that ( \pi ) (approximately 3.14) is a constant that relates the diameter of any circle to its circumference. Since the diameter ( d ) is twice the radius (i.e., ( d = 2r )), substituting ( d ) into the alternative formula for circumference ( C = \pi d ) leads to the expression ( C = \pi (2r) = 2\pi r ).

This formula is fundamental in geometry and applies to all circles, making it essential for solving various problems related to circular shapes. The other formulas relate to different aspects of circles or shapes entirely, which is why they are not applicable when calculating circumference. For example, ( πr² ) is the formula for the area of a circle, while the other options do not accurately represent the relationship needed for circumference.