Length of an arc
The length of an arc is the part of the circle's boundary between two points on the circle.
Practice This ConceptMain explanation
Teacher explanation
An arc is not the whole circumference. It is only a portion of the boundary, so its length is a fraction of 2πr depending on the central angle. This idea is very common in sector and shaded-region questions.
Example
If a circle has radius 10 cm and a central angle of 90°, the arc length is 90/360 × 2π × 10 = 5π cm.
Simple analogy
Arc is the curved border, not the filled floor.
Common confusion
Students often use sector area formula instead of arc length formula because both use the same angle fraction.
Exam tip
If the question says boundary part, curved edge, or only the arc, use arc length, not area.
Answer writing and exam use
1-mark use
Write the exact meaning of length of an arc in one clean line.
2-mark use
Define length of an arc and add one example or condition.
3-mark use
Explain length of an arc, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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