Arc length
SAT glossary · Math
Definition
The portion of a circle's circumference cut off by a central angle: the angle fraction times the circumference, e.g. 40/360· 2π(9)=2π. The trap is applying the fraction to the wrong whole — the sector-area computation instead of the circumference.
Arc length in plain English
Arc length is just a slice of a circle's outer edge (its circumference) — specifically, the piece cut off by a certain angle at the center. To find it, figure out what fraction of the full 360° that central angle represents, then multiply that fraction by the whole circle's circumference. For example, if your angle is 40° out of 360°, that's the fraction 40/360, and you multiply that by the circumference formula 2π r. The most common way this trips people up isn't the math itself — it's grabbing the wrong 'whole' to multiply by, like accidentally using the formula for a slice's AREA (a pie-slice-shaped region) instead of the length of its curved edge.
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