Circumference of a Circle: Questions and Solutions

Circumference of a circle Questions with answers presents methods and worked examples for finding the distance around one of the most important shapes in geometry. This guide reviews the standard formula: circumference of a circle = 2πr or πd and demonstrates its use through solved problems involving radius, diameter, and unit conversions. From straightforward computations to composite-shape and application problems, each solution focuses on clear steps, geometric reasoning and helpful shortcuts. Worked examples with brief explanations help strengthen understanding and exam preparation.

Table of Contents

• Circumference of a Circle Formula
• Solved Examples on Circumference of a Circle
• Practice Questions on Circumference of a Circle
• Frequently Asked Questions of Circumference of a Circle Questions

Circumference of a Circle Formula

The circumference of a circle is the total distance around its boundary.

• When radius (r) is known: C = 2πr

• When diameter (d) is known: C = πd   (since d = 2r)

Here, π is a constant with an approximate value of 22/7 or 3.14.

Read more: Circumference of a Circle

Solved Examples on Circumference of a Circle

Example 1: Find the circumference of a circular plate with radius 14 cm.

Solution: Given r = 14 cm

C = 2πr = 2 × 22/7 × 14 = 2 × 22 × 2 = 88 cm

Example 2: A circular clock has a diameter of 21 cm. Find its circumference.

Solution: Given d = 21 cm

C = πd = 22/7 × 21 = 22 × 3 = 66 cm

Example 3: A circular tabletop has a radius of 9 m. Find its circumference in terms of π.

Solution: Given r = 9 cm

C = 2πr = 2 × π × 9 = 18π m

Example 4: The diameter of a bicycle wheel is 70 cm. How many complete revolutions will it make while covering a distance of 2.2 km?

Solution: Given d = 70 cm

Total distance covered = 2.2 km 

Circumference of wheel = πd = 22/7 × 70 = 220 cm = 2.2 m

Distance to cover = 2.2 km = 2200 m

Number of revolutions = 2200 ÷ 2.2 = 1000 revolutions

Example 5: A circular garden has a radius of 21 m. Find the cost of fencing it at ₹15 per metre.

Solution: Given r = 21 cm

C = 2πr = 2 × 22/7 × 21 = 132 m

The cost of fencing it at ₹15 per metre

Total cost = 132 × ₹15 = ₹1,980

Example 6: Find the perimeter of a semicircular plot with radius 7 m.

Solution: Given r = 7 cm

Perimeter of semicircle = πr + 2r  (curved part + straight diameter)

= 22/7 × 7 + 2 × 7 = 22 + 14 = 36 m

Example 7: Assertion (A): A wire bent into a square of side 22 cm, when re-bent into a circle, will have a radius of 14 cm.

Reason (R): The perimeter of the square equals the circumference of the circle when the same wire is reshaped.

Solution:

Both A and R are true, and R correctly explains A.

Perimeter of square = 4 × 22 = 88 cm = circumference of circle.

2πr = 88 

⟹ r = 88 × 7/44 = 14 cm.

Example 8: A circular fountain in a park has a radius of 10.5 m. The municipal council wants to build a walking path around its edge and needs to order railing material sold only in whole metres. How many metres of railing should they order?

Solution:  Given r = 10.5 cm

C = 2πr = 2 × 22/7 × 10.5 = 66 m

The council should order 66 metres of railing.

Example 9: The minute hand of a wall clock is 10.5 cm long. Find the distance it travels in one complete hour.

Solution:  In one hour, the tip of the minute hand traces the full circumference of a circle with radius 10.5 cm.

C = 2πr = 2 × 22/7 × 10.5 = 66 cm

Example 10: The circumference of a circle exceeds its diameter by 16.8 cm. Find the radius of the circle.

Solution: 

C − d = 16.8

2πr − 2r = 16.8 

⟹ 2r(π − 1) = 16.8 

⟹ 2r(22/7 − 1) = 16.8

2r × 15/7 = 16.8 

⟹ r = 16.8 × 7 / 30 = 3.92 cm

Example 11: A car has wheels of diameter 80 cm. Find the number of complete revolutions made by a wheel in covering a distance of 1.408 km. (Use π = 22/7)

Solution: 

C = πd = 22/7 × 80 = 251.43 cm ≈ 2.5143 m

Distance = 1.408 km = 1408 m

Revolutions = 1408 ÷ 2.5143 ≈ 560 revolutions

Practice Questions on Circumference of a Circle

Q1. What is the circumference of a circle with radius 21 cm? (Use π = 22/7)

Q2. The diameter of a circle is 3.5 cm. Its circumference (using π = 22/7) is _____.

Q3. Which formula correctly finds the radius when the circumference C is known?

1. r = C/π

2. r = 2πC

3. r = C/2π

4. r = πC/2

Q4. If the circumference of a circle is 44 cm, what is its diameter?

Q5. The wheel of a bus has a diameter of 1.4 m. The distance it covers in 100 revolutions is:

1. 440 m

2. 220 m

3. 88 m

4. 140 m

Q6. Two circles have radii in the ratio 2 : 3. Their circumferences are in the ratio:

1. 2 : 3

2. 4 : 9

3. 3 : 2

4. 2 : 9

 

Get a free downloadable Circumference of a Circle worksheet with solved examples and practice questions to master circle formulas and improve your maths skills.

Circumference of a Circle Questions PDF Download