Circumference of a circle
The circumference is the total length of the boundary of a circle.
In one line: Circumference means circle's cover line, not inside space.
Practice This ConceptUnderstand it
Circumference tells us how much distance is needed to go once around the circle. It is the circle's outer edge, so it is a length measure, not an area measure. Students should always use linear units such as cm, m, or mm for the final answer.
Example
Formula and rule
Circumference = 2πr = πd, where r is radius and d is diameter.
Use this when the full boundary length is required.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
For r = 14 cm, circumference = 2π × 14 = 28π cm = 88 cm using π = 22/7.
Method you can reuse
- 1Read whether the question asks for boundary length.
- 2Identify radius or diameter from the data.
- 3Substitute in 2πr or πd.
- 4Simplify with the given value of π if needed.
- 5Write the answer in linear units.
Sketch it in your answer
Draw a circle, mark the radius from the centre to the boundary, and label the outer edge as the circumference.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
A round garden has radius 5 m. What does its circumference represent, and how would you calculate it?
Think first, then show answerHide answer
Common wrong answer
A common wrong answer is 154 cm for a radius 14 cm circle when the student accidentally uses area logic or forgets that circumference is a linear measure.
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
The circumference is the total length of the boundary of a circle.
- 2
Add for 2 marks
Example: If a circular plate has radius 7 cm, its circumference is 2πr = 14π cm, which is about 44 cm.
- 3
Add for 3 marks
Circumference tells us how much distance is needed to go once around the circle.
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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