What is the formula for calculating the arc length of a circle?

The formula for calculating the arc length of a circle is derived from the relationship between a circle's radius and the angle defining the arc, measured in degrees. The correct formula, L = 2πr(m⁰/360⁰), incorporates the radius of the circle (r) and the degree measure of the angle (m⁰) that subtends the arc.

In this formula, 2πr represents the total circumference of the circle, which corresponds to a full angle of 360 degrees. By multiplying the circumference by the fraction m⁰/360⁰, you obtain the length of the arc that corresponds to the angle m⁰. This correctly scales the total circumference down to just the portion representing the specified angle.

In contrast, other formulas presented do not represent arc length correctly. One option, for instance, uses πd instead of considering the entire circumference, which is not the proper relationship for arc length in this context. The formula L = rθ uses radians, which, while accurate for angles in radians, is not relevant here since the question specifies degrees. Lastly, L = πr²(m⁰/360⁰) misapplies the area formula of a sector, rather than focusing on the