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Circumference of a Circle

The circumference of a circle is the length of its curved boundary.

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Student-friendly explanation

A circle has no straight sides, so its perimeter is called circumference. It depends on the radius or diameter and uses pi, written as π.

How to write this in exams

  1. 1

    Start with the exact idea

    The circumference of a circle is the length of its curved boundary.

  2. 2

    Then show how to use it

    Check whether radius or diameter is given, choose C = 2πr or πd, substitute carefully, simplify, and write a length unit.

  3. 3

    Add one concrete example

    For radius 7 cm, circumference = 2πr = 2 × 22/7 × 7 = 44 cm.

  4. 4

    Avoid this incomplete answer

    154 cm for radius 7 cm is wrong because it is area, not circumference.

Definition

The circumference of a circle is the length of its curved boundary.

Example

For radius 7 cm, circumference = 2πr = 2 × 22/7 × 7 = 44 cm.

Rule to remember

C = 2πr or C = πd, where r is radius and d is diameter. π is irrational and is often approximated as 22/7 or 3.14.

Memory hook

Circumference is the circle's outside boundary.

Examples and method

Worked example

A wheel has radius 21 cm. One full rotation covers its circumference: 2 × 22/7 × 21 = 132 cm.

Method to apply

Check whether radius or diameter is given, choose C = 2πr or πd, substitute carefully, simplify, and write a length unit.

Diagram support

A circle diagram with radius and diameter marked helps students choose between 2πr and πd.

How CBSE asks it

Problems may ask distance covered by a wheel, fencing around a circular park, or circumference from diameter.

Avoid common mistakes

Common confusion

Students often use πr² and calculate area when the question asks for circumference.

Common wrong answer

154 cm for radius 7 cm is wrong because it is area, not circumference.

Exam tip

If the answer is boundary length, use 2πr or πd, not πr².

Quick check

What is the circumference of a circle with diameter 14 cm using π = 22/7?

The circumference is πd = 22/7 × 14 = 44 cm because diameter is given directly.

Answer writing and exam use

1-mark answer

The circumference of a circle is the length of its curved boundary.

2-mark answer

The circumference of a circle is the length of its curved boundary. C = 2πr or C = πd, where r is radius and d is diameter. π is irrational and is often approximated as 22/7 or 3.14. For radius 7 cm, circumference = 2πr = 2 × 22/7 × 7 = 44 cm.

3-mark answer

A circle has no straight sides, so its perimeter is called circumference. It depends on the radius or diameter and uses pi, written as π. C = 2πr or C = πd, where r is radius and d is diameter. π is irrational and is often approximated as 22/7 or 3.14. A wheel has radius 21 cm. One full rotation covers its circumference: 2 × 22/7 × 21 = 132 cm. Problems may ask distance covered by a wheel, fencing around a circular park, or circumference from diameter. 154 cm for radius 7 cm is wrong because it is area, not circumference.
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