Length of an arc
- CBSE · NCERT Class 10, Ch 11 Areas Related to Circles
The length of an arc is the distance along the curved edge of a circle between two points, a fraction of the whole circumference.
An arc is a piece of a circle's edge. The angle it makes at the centre tells you what fraction of the circle it is. The full edge is 2πr. So an arc with angle θ has length (θ/360) × 2πr. It is the curved edge of a sector.
A small example
A circle has radius 21 cm. An arc makes an angle of 60° at the centre. Its length is 60/360 × 2 × 22/7 × 21 = 1/6 × 132 = 22 cm. The whole edge of that sector is the arc plus two radii: 22 + 21 + 21 = 64 cm.
Where marks go
Question 36(iii)(A) of CBSE's 2026-27 Maths Basic sample paper asks for the tape needed around a black strip on a fan. The strip lies between arcs of radius 4 cm and 10 cm. In the 2026-27 Maths Basic marking scheme, the boundary is two straight pieces of 10 − 4 = 6 cm plus the two arcs.
The scheme gives 1 mark for that whole expression and 1 mark for the answer, 80/3 cm. An answer that counts only the arcs leaves out the straight edges of the boundary. Written working still lets each correct step count under step marking.
Sources
Facts last checked against these sources on 30 September 2026.
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