Length of an Arc and Sector Perimeter
Arc length is the length of a part of a circle's circumference, and sector perimeter is the arc length plus two radii.
In one line: Sector boundary has one curve and two radii.
Practice This ConceptUnderstand it
A sector is like a slice of a circle. Its curved part is only a fraction of the full circumference, decided by the central angle.
Example
Formula and rule
Arc length = θ/360 × 2πr.
Sector perimeter = arc length + 2r, where θ is the central angle in degrees.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
- 1For θ = 60° and r = 21 cm, arc length = 60/360 × 2 × 22/7 × 21 = 22 cm.
- 2Sector perimeter = 22 + 42 = 64 cm.
Method you can reuse
Sketch it in your answer
Draw a circle sector with central angle θ, radius r on both straight sides, and the curved arc labelled.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
Why is the perimeter of a sector not equal to only its arc length?
Think first, then show answerHide answer
Common wrong answer
22 cm for the perimeter of a 60°, 21 cm sector.
Why it loses marks: It gives only the arc length.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
Arc length is the length of a part of a circle's circumference, and sector perimeter is the arc length plus two radii.
- 2
Add for 2 marks
Example: For radius 14 cm and angle 90°, arc length = 90/360 × 2 × 22/7 × 14 = 22 cm; sector perimeter = 22 + 14 + 14 = 50 cm.
- 3
Add for 3 marks
A sector is like a slice of a circle.
Practice this concept with focused MCQs
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