What is the formula used to calculate the length of an arc in a circle?

The formula used to calculate the length of an arc in a circle is given by the relationship between the angle subtended by the arc at the center of the circle (θ, measured in radians) and the radius of the circle (r). Specifically, the length of the arc (L) can be expressed as:

[ L = θ × r ]

This formula arises from the fact that the arc length is proportional to both the radius and the angle. When the angle is in radians, 1 radian is defined as the angle subtended at the center of a circle that creates an arc whose length is equal to the radius. Therefore, if you multiply the angle (in radians) by the radius, you get the exact length of the arc.

The other options represent different geometrical concepts: the 2πr formula calculates the circumference of the entire circle (which represents the length if θ equals 2π), while πr² represents the area of a circle. The formula θ/r does not apply directly to arc length in standard terms, as it does not unite the two necessary components (angle in radians and radius) for finding arc length.