In a circle, which term represents the length along the circumference corresponding to a central angle?

• A. Sector Area
• B. Arc length
• C. Sine
• D. Radius

Answer: (B)

Arc length is the length along the circle’s edge that corresponds to a central angle. If the circle has radius r and the central angle is θ measured in radians, the arc length s is rθ. This makes sense because the whole circumference 2πr matches a full angle of 2π radians, so s = (θ/2π)·2πr = rθ. If the angle is in degrees, arc length is s = (θ/360)·2πr. This is why the quantity described is arc length: it’s the portion of the circumference set off by the central angle. The sector area, by contrast, concerns the area of the region inside that angle, not the boundary length; sine is a trigonometric ratio; and the radius is the straight line from the center to the circle, not a length along the edge.