How can the circumference of a circle be calculated?

The calculation of a circle's circumference is based on a relationship involving its radius (r) and diameter (d). The correct formula, which states that the circumference equals 2π times the radius or π times the diameter, reflects the inherent properties of a circle. This relationship defines how the circumference is directly proportional to the size of the circle, with π acting as a constant ratio that relates the circle's diameter to its circumference.

The formula 2πr is derived from the fact that the diameter of a circle is twice the length of the radius, making both forms—2πr and πd—equivalent ways to express the circumference. This understanding is essential in geometry, as it encapsulates key concepts of circular measurements.

Other options presented do not accurately describe how circumference is calculated. One option incorrectly suggests using the radius in a squared context, which is a formula related to the area of a circle rather than its circumference. Another suggests using base and height, which pertains to rectangles and other polygons, thus not applicable to circles at all.