Concept 11.2
Length of an Arc
Source: NCERT Mathematics, Class 106 minute lesson
Formal statement
The length of the arc of a sector of angle θ is (θ/360) × 2πr.
The intuition
The arc is the same slice, measured around the edge instead of across the inside. So it takes the same fraction, θ/360, of the full circumference 2πr.
The two formulas share their fraction and differ in their whole: area uses πr², length uses 2πr. Mixing up the wholes is the usual mistake.
The attention
Look at which whole the fraction is taken of: the circumference.
Arc = θ/360 × 2πr not θ/360 × πr²
Look hereNot here
- Look here
- The whole circumference, 2πr. An arc is a length, so it is a fraction of the circle's length, 2πr.
- Not here
- The whole area, πr². πr² is an area. Using it gives square units for a length, a sure sign something is wrong.
- What it teaches
- Check the units: a length can't come from an area.