What mathematical expression is used to calculate the circumference of a circle?

The mathematical expression used to calculate the circumference of a circle is 2πr. This formula derives from the relationship of a circle's radius to its circumference, where 'r' represents the radius of the circle and π (pi) is a constant approximately equal to 3.14. The circumference can be seen as the total distance around the circle, and since a diameter is twice the radius (d = 2r), when this relationship is substituted into the formula for the circumference, it gives the formula of 2πr.

The other options represent different aspects of circle geometry. The area of a circle, for instance, is calculated with πr². The expression r²/π does not have a standard geometric interpretation related to circumference. The expression πr could be considered as a part of other equations, but it does not represent the full distance around the circle. Therefore, 2πr is the correct expression for the circumference, as it accurately combines the radius with the constant π in the context of circular geometry.