Circumference of a Circle (Introduction)
The circumference of a circle is the distance around it. Just as the perimeter is the boundary of a rectangle, the circumference is the boundary of a circle.
If you wrap a string around a circular bangle and then straighten it, the length of the string is the circumference. In Class 5, you will learn the relationship between the circumference and the diameter of a circle, and discover the special number π (pi).
This is an introductory topic. You will use the approximate value π ≈ 3.14 or π ≈ 22/7 for calculations.
What is Circumference of a Circle (Introduction) - Class 5 Maths (Geometry)?
The circumference is the total length of the boundary of a circle. It is measured in linear units (cm, m, etc.).
Key terms:
- Radius (r): Distance from the centre to any point on the circle.
- Diameter (d): Distance across the circle through the centre. Diameter = 2 × radius.
- π (pi): A special number that is the ratio of circumference to diameter for every circle. π ≈ 3.14 ≈ 22/7.
Circumference of a Circle (Introduction) Formula
Circumference = π × d = π × 2r = 2πr
π ≈ 3.14 or 22/7
Relationship: For every circle, Circumference ÷ Diameter = π (always approximately 3.14).
Types and Properties
Two forms of the circumference formula:
- When diameter is given: Circumference = π × d
- When radius is given: Circumference = 2 × π × r
Choosing the value of π:
- Use 22/7 when the diameter or radius is a multiple of 7 (makes division easy).
- Use 3.14 for all other cases.
Solved Examples
Example 1: Example 1: Circumference from Diameter
Problem: Find the circumference of a circle with diameter 14 cm. (Use π = 22/7)
Solution:
Step 1: Circumference = π × d
Step 2: = 22/7 × 14 = 22 × 2 = 44 cm
Answer: The circumference is 44 cm.
Example 2: Example 2: Circumference from Radius
Problem: Find the circumference of a circle with radius 10 cm. (Use π = 3.14)
Solution:
Step 1: Circumference = 2 × π × r
Step 2: = 2 × 3.14 × 10 = 62.8 cm
Answer: The circumference is 62.8 cm.
Example 3: Example 3: Finding Diameter from Circumference
Problem: The circumference of a circular garden is 88 m. Find its diameter. (Use π = 22/7)
Solution:
Step 1: Circumference = π × d
Step 2: 88 = 22/7 × d
Step 3: d = 88 × 7/22 = 616/22 = 28 m
Answer: The diameter is 28 m.
Example 4: Example 4: Bangle Circumference
Problem: Aditi’s bangle has a diameter of 7 cm. What is its circumference?
Solution:
Step 1: Circumference = π × d = 22/7 × 7 = 22 cm
Answer: The circumference of the bangle is 22 cm.
Example 5: Example 5: Circular Running Track
Problem: A circular running track has a radius of 35 m. How far does Rahul run in one complete round? (Use π = 22/7)
Solution:
Step 1: One round = circumference = 2 × 22/7 × 35
Step 2: = 2 × 22 × 5 = 220 m
Answer: Rahul runs 220 m in one round.
Example 6: Example 6: Distance in Multiple Rounds
Problem: A circular park has a diameter of 42 m. Meera jogs 3 rounds. What is the total distance?
Solution:
Step 1: Circumference = 22/7 × 42 = 132 m
Step 2: Total distance = 3 × 132 = 396 m
Answer: Meera jogs 396 m in total.
Example 7: Example 7: Wheel Problem
Problem: A bicycle wheel has a diameter of 70 cm. How far does the bicycle travel in 10 rotations of the wheel?
Solution:
Step 1: Circumference = 22/7 × 70 = 220 cm
Step 2: Distance in 10 rotations = 10 × 220 = 2,200 cm = 22 m
Answer: The bicycle travels 22 m.
Example 8: Example 8: Finding Radius from Circumference
Problem: A circular plate has a circumference of 31.4 cm. Find its radius. (Use π = 3.14)
Solution:
Step 1: Circumference = 2πr
Step 2: 31.4 = 2 × 3.14 × r = 6.28 × r
Step 3: r = 31.4 ÷ 6.28 = 5 cm
Answer: The radius is 5 cm.
Example 9: Example 9: Discovering Pi
Problem: Dev measures three circular objects. Object A: circumference 22 cm, diameter 7 cm. Object B: circumference 44 cm, diameter 14 cm. Object C: circumference 66 cm, diameter 21 cm. Calculate circumference ÷ diameter for each. What do you notice?
Solution:
A: 22 ÷ 7 = 3.14...
B: 44 ÷ 14 = 3.14...
C: 66 ÷ 21 = 3.14...
Answer: The ratio is always approximately 3.14 (π) for every circle.
Example 10: Example 10: Wire Bent into a Circle
Problem: A wire 44 cm long is bent into a circle. Find the radius of the circle. (Use π = 22/7)
Solution:
Step 1: Wire length = circumference = 44 cm
Step 2: 2πr = 44
Step 3: r = 44 ÷ (2 × 22/7) = 44 × 7/44 = 7 cm
Answer: The radius is 7 cm.
Real-World Applications
Where do we use circumference?
- Wheels and tyres: Finding how far a vehicle travels per rotation of its wheel.
- Circular tracks: Calculating the distance of one lap on a running track or cycling track.
- Bangles and rings: Measuring the size of circular jewellery.
- Fencing: Finding how much fencing is needed around a circular garden or pond.
- Clock faces: The tip of a clock hand traces a circumference every hour.
Key Points to Remember
- Circumference = distance around a circle = π × diameter = 2πr.
- π (pi) ≈ 3.14 ≈ 22/7. It is the ratio of circumference to diameter for every circle.
- Diameter = 2 × radius. Radius = diameter ÷ 2.
- Use π = 22/7 when the diameter or radius is a multiple of 7.
- One full rotation of a wheel covers a distance equal to its circumference.
- Circumference is measured in linear units (cm, m), not square units.
- To find diameter from circumference: d = circumference ÷ π.
Practice Problems
- Find the circumference of a circle with diameter 21 cm. (Use π = 22/7)
- A circle has a radius of 5 cm. Find its circumference. (Use π = 3.14)
- The circumference of a circular pond is 176 m. Find its diameter. (Use π = 22/7)
- A wheel has a radius of 28 cm. How far does it travel in 50 rotations?
- Priya wraps a ribbon around a circular cake of diameter 28 cm. What length of ribbon does she need?
- A circular playground has circumference 440 m. Arjun runs 5 laps. What total distance does he cover?
- A wire 88 cm long is bent into a circle. Find its diameter.
- Which has a greater circumference: a circle with diameter 20 cm or a circle with radius 12 cm?
Frequently Asked Questions
Q1. What is circumference?
Circumference is the distance around a circle. It is the circle’s perimeter. If you walk along the edge of a circular track, you walk the circumference.
Q2. What is pi (π)?
π is a special number approximately equal to 3.14 or 22/7. It is the ratio of the circumference to the diameter for every circle, regardless of size.
Q3. What is the formula for circumference?
Circumference = π × diameter = 2 × π × radius. Use whichever form matches the information given in the problem.
Q4. When should I use 22/7 and when 3.14?
Use 22/7 when the diameter or radius is a multiple of 7 (like 7, 14, 21, 28, 35). Use 3.14 for other values. Both give approximate results.
Q5. What is the difference between circumference and area of a circle?
Circumference measures the length of the boundary (in cm, m). Area measures the surface enclosed by the circle (in cm², m²). They use different formulas.
Q6. How does a wheel problem relate to circumference?
One full rotation of a wheel covers a distance equal to the circumference of the wheel. So distance = number of rotations × circumference.
Q7. Can I find the radius if circumference is given?
Yes. Radius = circumference ÷ (2π). Divide the circumference by 2 × 3.14 (or 2 × 22/7).
Q8. Is circumference taught in NCERT Class 5?
Basic introduction to circumference and the concept of π is introduced at the Class 5 level. Detailed study continues in higher classes.
Q9. What is the relationship between diameter and radius?
Diameter is always twice the radius: d = 2r. Radius is half the diameter: r = d/2.
Q10. Is π exactly 3.14?
No. π is an irrational number with infinite non-repeating decimal places (3.14159265...). We use 3.14 or 22/7 as convenient approximations for calculations.
