Which formula is used to calculate the circumference of a circle?

The circumference of a circle can be calculated using two equivalent formulas, but the most commonly recognized forms involve the radius (r) or the diameter (d). The correct choice, which states that the circumference is equal to 2 times pi times the radius (C = 2πr), is based on the relationship between the radius of the circle and its circumference.

When you consider that the diameter (d) is twice the radius (d = 2r), the formula for circumference can also be expressed as C = πd. This demonstrates that both formulas are valid; however, the one focusing on the radius emphasizes the circle's dimensions directly related to its radial measurement.

The formula C = r²π incorrectly incorporates the radius, as the circumference does not depend on the area (which involves squaring the radius) but rather on the linear distance around the circle's edge. The formula C = 2r is also inaccurate, as it omits the crucial factor of π, which is necessary to account for the circular nature of the shape.

Therefore, the most accurate and widely used formula that corresponds to the measurement of circumference in relation to the radius is indeed C = 2πr.