⭕ Class 7 · Mensuration

Circles: Area and Circumference for Class 7: notes, worked examples and practice

The circumference is the distance around a circle and the area is the space inside it. Both come from the radius and the special number π.

Updated 21 October 2026. Every worked example and answer on this page is checked by automated tests.

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Notes

Circles: Area and Circumference: what you need to know

Chapter names and order differ by board and textbook edition, so follow your own textbook for the order.

Parts of a circle

The radius is the distance from the centre to the edge. The diameter passes through the centre and is twice the radius. The circumference is the length of the boundary.

The number π

For every circle, circumference ÷ diameter is the same number, called π. Its value is about 3.14, and many problems use 22/7.

Circumference

C = 2πr = πd. With π = 22/7 and r = 7 cm, C = 2 × 22/7 × 7 = 44 cm.

Area

A = πr². With π = 22/7 and r = 14 cm, A = 22/7 × 14 × 14 = 616 cm².

Use the right value of π

Use 22/7 when the radius is a multiple of 7 and 3.14 otherwise, unless the question tells you which to use.

Formulas and rules to remember

C = 2πr = πd
A = πr²
d = 2r
π ≈ 22/7 or 3.14

Solved examples

Example 1

Find the circumference of a circle of radius 7 cm (use π = 22/7).

C = 2 × 22/7 × 7.
= 44.

Answer: 44 cm

Example 2

Find the area of a circle of radius 14 cm (use π = 22/7).

A = 22/7 × 14 × 14.
= 22 × 2 × 14 = 616.

Answer: 616 cm²

Example 3

A circle has diameter 10 cm. Find its circumference (use π = 3.14).

C = π × d = 3.14 × 10.
= 31.4.

Answer: 31.4 cm

Example 4

A wheel has diameter 70 cm. How many full turns does it make to cover 22 m? (π = 22/7)

Circumference = 22/7 × 70 = 220 cm.
22 m = 2200 cm.
Turns = 2200 ÷ 220 = 10.

Answer: 10 turns

Avoid these

Common mistakes

Using the diameter as the radius

In A = πr² the r is the radius. If you are given the diameter, halve it first.

Mixing up circumference and area

Circumference is a length (cm). Area is square units (cm²).

Forgetting to square the radius

A = π × r × r, not π × r × 2.

10 practice questions with answers

Try each question on paper first, then tap it to check your answer. The questions are generated by code and each answer is checked.

Circumference of a circle with radius 6 cm (use 3.14):
Answer: 37.68
Circumference of a circle with radius 9 cm (use 3.14):
Answer: 56.52
Circumference of a circle with radius 4 cm (use 3.14):
Answer: 25.12
Circumference of a circle with radius 5 cm (use 3.14):
Answer: 31.4
Area of a circle with radius 1 cm (use 3.14):
Answer: 3.14
Area of a circle with radius 6 cm (use 3.14):
Answer: 113.04
Area of a circle with radius 7 cm (use 3.14):
Answer: 153.86
Area of a circle with radius 5 cm (use 3.14):
Answer: 78.5
Area of a circle with radius 2 cm (use 3.14):
Answer: 12.56
Area of a circle with radius 10 cm (use 3.14):
Answer: 314

More practice

Printable worksheets (PDF with answers)

Circles, circumference and area (Grade 7)

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FAQ

Circles: Area and Circumference Class 7: questions students ask

What is the formula for the area of a circle?

A = πr², where r is the radius.

What is the formula for circumference?

The circumference of a circle is C = 2πr or C = πd, where r is the radius and d is the diameter.

Should I use 22/7 or 3.14 for π?

Use whichever the question says. If it does not say, use 22/7 when the radius is a multiple of 7, otherwise 3.14.

What is the relation between radius and diameter?

The diameter is twice the radius.

Which board is this circles: area and circumference page for?

It covers the ideas taught in CBSE, ICSE and state-board maths. Chapter names and order differ by board and textbook edition, so follow your own textbook for the exact order.

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