Circles — Radius, Diameter, Circumference

Mathematics

Class 5 | CBSE, NCERT & ICSE

Learning Objectives

Understand what a circle is and how it differs from other shapes
Identify and name all parts of a circle (centre, radius, diameter, chord, arc, circumference, semicircle, sector, segment)
Understand the relationship between radius and diameter (d = 2r)
Learn the concept of circumference and its formula (C = π × d = 2 × π × r)
Get introduced to π (pi) as approximately 3.14 or 22/7
Draw circles using a compass with a given radius
Understand concentric circles and their real-life examples
Solve word problems involving circles using Indian context

Introduction — Circles All Around Us

Look around you — circles are everywhere! The wheels of your bicycle, the ₹1, ₹2, and ₹5 coins in your pocket, the bangles your mother wears, the face of a clock, the Ashoka Chakra on our Indian flag, ISRO's satellite dishes, manhole covers on the road, the Olympic rings, a cricket ball's cross-section, the base of a glass — all of these are circles!

A circle is one of the most important shapes in mathematics. Unlike squares or triangles, a circle has no corners and no straight sides. It is a perfectly round shape. In this chapter, we will learn about the different parts of a circle, how to measure it, and how to draw one using a compass. We will also discover a very special number called π (pi) that helps us find the distance around any circle!

Image needed: A collage of real-life circles found in India — ₹5 coin, bicycle wheel, Ashoka Chakra from Indian flag, bangle, clock face, manhole cover, satellite dish, Olympic rings. Each labelled clearly.
Style: Colourful flat illustration, child-friendly, arranged in a grid with labels
Size: 800×450px

What is a Circle?

A circle is a closed curve in which every point on the curve is at the same distance from a fixed point called the centre.

Definition

A circle is a set of all points in a plane that are equidistant (same distance) from a fixed point.
The fixed point is called the centre of the circle.
The fixed distance from the centre to any point on the circle is called the radius.

How is a Circle Different from Other Shapes?

Property	Circle	Triangle / Square / Rectangle
Sides	No straight sides (one continuous curved boundary)	3 or 4 straight sides
Corners (Vertices)	No corners	3 or 4 corners
Angles	No angles	Has angles at each vertex
Is it a polygon?	No — a circle is NOT a polygon	Yes
Symmetry	Infinite lines of symmetry	Limited lines of symmetry

Think About It: A polygon is a closed figure made of straight line segments. Since a circle has NO straight sides, it is not a polygon. It is a special curved shape!

Parts of a Circle

A circle has many important parts. Let us learn each one carefully:

Image needed: A large, clearly labelled diagram of a circle showing ALL parts: centre (O), radius (OA), diameter (AB passing through centre), chord (CD not passing through centre), arc (minor arc and major arc), circumference (the boundary), semicircle, sector (shaded pie slice), and segment (shaded region between chord and arc). Each part labelled with arrows and different colours.
Style: Clean educational diagram, bright colours for each part, child-friendly labels with bold text
Size: 700×700px

1. Centre

The centre is the fixed point inside the circle from which every point on the circle is the same distance away. It is usually marked as O. The centre is NOT on the circle — it is inside it.

2. Radius (plural: Radii)

The radius is the distance from the centre to any point on the circle. A circle has infinitely many radii, and they are all equal in length.

Example: If the centre of a circle is O and point A is on the circle, then OA is a radius. If point B is also on the circle, then OB is also a radius — and OA = OB.

3. Diameter

The diameter is a straight line that passes through the centre and has both its endpoints on the circle. It is the longest chord of a circle.

Important Relationship

Diameter = 2 × Radius (d = 2r)
Radius = Diameter ÷ 2 (r = d/2)
The diameter divides the circle into two equal halves (semicircles).

4. Chord

A chord is a straight line segment with both endpoints on the circle. A chord does NOT need to pass through the centre.

If a chord passes through the centre, it becomes a diameter.
The diameter is the longest possible chord of any circle.
There can be infinitely many chords in a circle.

5. Arc

An arc is a part (portion) of the circumference. When a chord divides the circle, it creates two arcs:

Minor Arc: The shorter arc (smaller part of the circle).
Major Arc: The longer arc (larger part of the circle).

6. Circumference

The circumference is the total distance around the circle. It is like the perimeter of a circle. We will learn how to calculate it using a special formula later in this chapter.

7. Semicircle

A semicircle is exactly half of a circle. When a diameter divides a circle into two equal parts, each part is called a semicircle. The word "semi" means "half."

8. Sector

A sector is the region enclosed between two radii and an arc. It looks like a slice of pizza or a slice of cake!

Minor Sector: The smaller pizza slice.
Major Sector: The larger region.

9. Segment

A segment is the region between a chord and the arc it cuts off.

Minor Segment: The smaller region between the chord and the minor arc.
Major Segment: The larger region between the chord and the major arc.

Summary Table — Parts of a Circle

Part	What It Is	Key Fact
Centre (O)	Fixed point inside the circle	All radii are measured from here
Radius (r)	Line from centre to circle boundary	All radii are equal; r = d/2
Diameter (d)	Line through centre, both ends on circle	d = 2r; longest chord
Chord	Line with both ends on circle	Diameter is the longest chord
Arc	Part of the circumference	Minor arc (small) and Major arc (large)
Circumference	Total distance around the circle	C = π × d = 2πr
Semicircle	Half of a circle	Bounded by a diameter and an arc
Sector	Region between two radii and an arc	Looks like a pizza slice
Segment	Region between a chord and an arc	Minor and Major segments

Relationship Between Radius and Diameter

The relationship between the radius and the diameter is one of the most important facts about circles:

The Golden Rule

Diameter = 2 × Radius → d = 2r
Radius = Diameter ÷ 2 → r = d/2

Image needed: A visual showing a circle with both the radius and diameter clearly marked. The diameter line goes from one edge through the centre O to the other edge. Two radius lines are shown (from centre to edge). Labels show d = 2r with arrows. A second smaller diagram shows the equation visually: one diameter line equals two radius lines placed end to end.
Style: Clean diagram with bright colours, bold labels, educational
Size: 650×400px

Finding Diameter from Radius

Example 1: The radius of a circle is 7 cm. Find the diameter.
Solution: d = 2 × r = 2 × 7 = 14 cm

Example 2: A circular bangle has a radius of 3.5 cm. What is its diameter?
Solution: d = 2 × 3.5 = 7 cm

Example 3: The radius of the Ashoka Chakra on the Indian flag is 4.5 cm in a standard-size flag. Find the diameter.
Solution: d = 2 × 4.5 = 9 cm

Finding Radius from Diameter

Example 4: The diameter of a ₹5 coin is approximately 2.3 cm. Find its radius.
Solution: r = d ÷ 2 = 2.3 ÷ 2 = 1.15 cm

Example 5: A circular garden has a diameter of 28 metres. Find the radius.
Solution: r = 28 ÷ 2 = 14 metres

Example 6: The diameter of a circular well in Rajasthan is 3.5 metres. What is the radius?
Solution: r = 3.5 ÷ 2 = 1.75 metres

Practice Table

Object	Radius (r)	Diameter (d = 2r)
₹1 coin	1.1 cm	2.2 cm
₹2 coin	1.25 cm	2.5 cm
₹5 coin	1.15 cm	2.3 cm
Cricket ball	3.6 cm	7.2 cm
Bicycle wheel	34 cm	68 cm
Circular park	50 m	100 m

Think About It: Can a radius ever be longer than a diameter of the same circle? No! The diameter is always exactly twice the radius. So the diameter is always longer than the radius.

Circumference — The Distance Around a Circle

The circumference of a circle is the total distance around the boundary of the circle. It is like the perimeter, but for a circle. If an ant walks along the edge of a circular plate and comes back to where it started, the distance it covers is the circumference.

Image needed: An illustration of a small ant walking along the edge of a circle (like walking on a circular track). The path the ant takes is highlighted in a bright colour. An arrow shows the direction of movement. A label says "Circumference = distance the ant walks to go all the way around."
Style: Cute child-friendly illustration, cartoon ant, colourful circle
Size: 500×500px

Discovering Pi (π)

Long ago, mathematicians noticed something amazing. When they divided the circumference of ANY circle by its diameter, they always got the same number — approximately 3.14. This special number is called π (pi).

What is Pi (π)?

π is a special mathematical constant.
π ≈ 3.14 (approximately 3.14)
π can also be written as 22/7 (a close fraction).
π = Circumference ÷ Diameter (for ANY circle!)
The actual value of π goes on forever: 3.14159265358... (it never ends and never repeats!)

Did You Know? The great Indian mathematician Aryabhata (born 476 AD in Patna, Bihar) calculated the value of π as 3.1416 — an incredibly accurate result for that time! India has a proud history of mathematical discoveries.

The Circumference Formula

Since π = Circumference ÷ Diameter, we can rearrange this to find the circumference:

Circumference Formulas

C = π × d (Circumference = pi × diameter)
C = 2 × π × r (Circumference = 2 × pi × radius)
Use π ≈ 3.14 or π ≈ 22/7 in calculations.

Solved Examples — Finding Circumference

Example 1: Find the circumference of a circle with diameter 14 cm. (Use π = 22/7)
Solution:
C = π × d
C = 22/7 × 14
C = 22 × 2 = 44 cm

Example 2: Find the circumference of a circle with radius 7 cm. (Use π = 22/7)
Solution:
C = 2 × π × r
C = 2 × 22/7 × 7
C = 2 × 22 = 44 cm

Example 3: A circular garden has a radius of 21 metres. Meena wants to put a fence around it. How much fencing wire does she need? (Use π = 22/7)
Solution:
Circumference = 2 × π × r
C = 2 × 22/7 × 21
C = 2 × 22 × 3
C = 132 metres
Meena needs 132 metres of fencing wire.

Example 4: The diameter of a bicycle wheel is 70 cm. How far does the bicycle travel in one complete rotation of the wheel? (Use π = 22/7)
Solution:
In one complete rotation, the wheel covers a distance equal to its circumference.
C = π × d = 22/7 × 70 = 22 × 10 = 220 cm = 2.2 metres

Example 5: A circular plate has a radius of 10 cm. Find its circumference. (Use π = 3.14)
Solution:
C = 2 × π × r
C = 2 × 3.14 × 10
C = 62.8 cm

Example 6: Arjun runs around a circular track of diameter 56 metres. If he completes 5 rounds, how much total distance does he cover? (Use π = 22/7)
Solution:
Circumference of track = π × d = 22/7 × 56 = 22 × 8 = 176 metres (per round)
Total distance for 5 rounds = 176 × 5 = 880 metres

Drawing Circles with a Compass

A compass (also called a pair of compasses) is a tool used to draw perfect circles. It has two arms — one with a sharp needle point and the other with a pencil.

Steps to Draw a Circle

Step	What to Do
1	Decide the radius of the circle you want to draw.
2	Open the compass to the required radius using a ruler. For example, if you want a radius of 4 cm, set the distance between the needle and pencil tip to 4 cm.
3	Place the needle (sharp point) firmly on the paper. This point becomes the centre of your circle.
4	Hold the compass at the top knob and rotate it slowly in one direction (clockwise or anticlockwise) until the pencil draws a complete circle back to the starting point.
5	Mark the centre with a dot and label it 'O'. Your circle is ready!

Practice Task: Draw a circle with radius 3 cm. Then draw another circle with radius 5 cm using the same centre. You have made concentric circles!

Tips for Using a Compass:

Keep the needle point steady — don't let it slip.
Hold the compass at the top and lean it slightly in the direction of rotation.
Make sure the pencil tip is sharp for a clean line.
Don't press too hard — let the pencil glide smoothly.

Concentric Circles

Concentric circles are circles that share the same centre but have different radii. They look like circles inside circles — like a target board!

Image needed: An illustration showing concentric circles with the same centre O. Three or four circles of different sizes sharing the same centre point. Next to it, real-life examples: an archery target (colourful rings), the Ashoka Chakra (24 spokes with concentric structure), a dartboard, ripples in water when a stone is dropped.
Style: Clean diagram on left, colourful real-life examples on right, labelled
Size: 750×400px

Real-Life Examples of Concentric Circles

Archery target: The rings of an archery target are concentric circles. The bullseye is the innermost circle.
Tree trunk rings: When you cut a tree trunk, the growth rings are concentric circles. Each ring represents one year of growth!
Ripples in water: When you drop a stone in a pond, the ripples that spread out are concentric circles.
Dartboard: The scoring zones on a dartboard are concentric circles.
CDs and DVDs: The data tracks on a CD are arranged in concentric circles.
Rangoli patterns: Many Indian rangoli designs use concentric circles as a base pattern.

Example: Akriti draws three concentric circles with radii 2 cm, 4 cm, and 6 cm. What are the diameters of each circle?
Solution:
Circle 1: d = 2 × 2 = 4 cm
Circle 2: d = 2 × 4 = 8 cm
Circle 3: d = 2 × 6 = 12 cm
All three circles have the same centre but different sizes.

Word Problems — Circles in Real Life

Problem 1: A circular playground in Arjun's school has a diameter of 42 metres. The school wants to plant flowers along the boundary. What is the length of the boundary? (Use π = 22/7)
Solution:
The length of the boundary = Circumference
C = π × d = 22/7 × 42 = 22 × 6 = 132 metres

Problem 2: Dhruv's father bought a circular table with radius 70 cm. He wants to put a decorative border (lace) around the edge of the table. How much lace does he need? (Use π = 22/7)
Solution:
C = 2 × π × r = 2 × 22/7 × 70 = 2 × 220 = 440 cm = 4.4 metres

Problem 3: A circular well in a village in Rajasthan has a diameter of 3.5 metres. What is the circumference of the well? (Use π = 22/7)
Solution:
C = π × d = 22/7 × 3.5 = 22/7 × 7/2 = 22/2 = 11 metres

Problem 4: The wheel of a bullock cart has a radius of 35 cm. How many complete rotations will the wheel make to cover a distance of 440 metres? (Use π = 22/7)
Solution:
Circumference of wheel = 2 × π × r = 2 × 22/7 × 35 = 2 × 110 = 220 cm = 2.2 m
Number of rotations = Total distance ÷ Circumference = 440 ÷ 2.2 = 200 rotations

Problem 5: Meena made a circular rangoli with a radius of 1.4 metres for Diwali. She decorated the outer edge with coloured powder. How much coloured powder border did she create? (Use π = 22/7)
Solution:
C = 2 × π × r = 2 × 22/7 × 1.4 = 2 × 22/7 × 14/10 = 2 × 22 × 2/10 = 88/10 = 8.8 metres

Key Words

Term	Meaning
Circle	A closed curve where every point is the same distance from the centre
Centre (O)	The fixed point inside a circle from which all points on the circle are equidistant
Radius (r)	Distance from the centre to any point on the circle
Diameter (d)	A line passing through the centre with both ends on the circle; d = 2r
Chord	A line segment with both endpoints on the circle
Arc	A part of the circumference (minor arc = smaller, major arc = larger)
Circumference (C)	The total distance around the circle; C = πd = 2πr
Pi (π)	A constant ≈ 3.14 or 22/7; ratio of circumference to diameter
Semicircle	Half of a circle, formed when a diameter divides a circle
Sector	Region between two radii and an arc (pizza slice shape)
Segment	Region between a chord and an arc
Concentric Circles	Circles with the same centre but different radii
Compass	A tool used to draw circles

Key Points to Remember

A circle is NOT a polygon — it has no straight sides, no vertices, no angles.
Diameter = 2 × Radius (d = 2r) and Radius = Diameter ÷ 2 (r = d/2).
All radii of the same circle are equal. All diameters of the same circle are equal.
The diameter is the longest chord of a circle.
Circumference = π × d = 2 × π × r where π ≈ 3.14 or 22/7.
π (pi) is the ratio of circumference to diameter — it is the same for ALL circles!
The Indian mathematician Aryabhata calculated π ≈ 3.1416 in the 5th century AD.
A circle has infinite lines of symmetry — every diameter is a line of symmetry.
Concentric circles share the same centre but have different radii.
In one rotation, a circular wheel covers a distance equal to its circumference.

Finished learning? Now test what you know!

🎯 Quick Quiz — Test Yourself!

Answer these questions right here. You get instant feedback — no paper needed!

Score: 0 / 8

1. The distance from the centre of a circle to any point on it is called the:

The radius runs from the centre to the edge.

2. The diameter of a circle is:

Diameter = 2 × radius.

3. The distance all the way around a circle is called its:

The circumference is the perimeter (boundary length) of a circle.

4. The value of π (pi) is approximately:

π ≈ 3.14 (or 22/7).

5. A circle has a radius of 7 cm. What is its diameter? (cm)

Diameter = 2 × radius = 2 × 7 = 14 cm.

6. A circle has a diameter of 10 cm. What is its radius? (cm)

Radius = diameter ÷ 2 = 10 ÷ 2 = 5 cm.

7. Circumference = π × diameter. Using π = 22/7, find the circumference of a circle with diameter 14 cm. (cm)

C = (22/7) × 14 = 22 × 2 = 44 cm.

8. A straight line joining any two points on a circle (not through the centre) is called a ______.

A chord joins two points on the circle. The longest chord is the diameter.

Practice Questions

A. Fill in the Blanks:

1. A circle is a closed curve where every point is at the same distance from the .

2. The distance from the centre to any point on the circle is called the .

3. Diameter = × Radius.

4. The longest chord of a circle is the .

5. The total distance around a circle is called the .

6. π (pi) is approximately equal to or .

7. Half of a circle is called a .

8. Circles with the same centre but different radii are called circles.

9. A circle has lines of symmetry.

10. The Indian mathematician calculated the value of π in the 5th century.

B. Find the Diameter (given Radius):

1. Radius = 6 cm → Diameter =

2. Radius = 9.5 cm → Diameter =

3. Radius = 14 m → Diameter =

4. Radius = 3.5 m → Diameter =

5. Radius = 21 cm → Diameter =

C. Find the Radius (given Diameter):

1. Diameter = 18 cm → Radius =

2. Diameter = 7 m → Radius =

3. Diameter = 44 cm → Radius =

4. Diameter = 5.6 m → Radius =

5. Diameter = 100 cm → Radius =

D. Find the Circumference (Use π = 22/7):

1. Diameter = 14 cm → C =

2. Radius = 7 m → C =

3. Diameter = 28 cm → C =

4. Radius = 21 m → C =

5. Diameter = 35 cm → C =

E. True or False:

1. A circle is a polygon.

2. The diameter is the longest chord of a circle.

3. All radii of a circle are equal.

4. A chord always passes through the centre.

5. π is exactly equal to 3.14.

6. A semicircle is half of a circle.

7. The diameter is always twice the radius.

8. Concentric circles have the same radius.

F. Choose the Correct Answer (MCQ):

1. The radius of a circle is 10 cm. What is the diameter?

a) 5 cm b) 10 cm c) 20 cm d) 40 cm

2. The value of π is approximately:

a) 3.41 b) 3.14 c) 2.14 d) 4.14

3. Which of these is the longest chord of a circle?

a) Radius b) Arc c) Diameter d) Sector

4. If the diameter of a wheel is 7 cm, its circumference is: (π = 22/7)

a) 44 cm b) 22 cm c) 14 cm d) 11 cm

5. How many lines of symmetry does a circle have?

a) 1 b) 4 c) 8 d) Infinite

G. Name the Parts of a Circle:

1. A line segment from the centre to any point on the circle:

2. A line that passes through the centre with both ends on the circle:

3. A line segment with both ends on the circle (not necessarily through centre):

4. The boundary (distance around) the circle:

5. A region between two radii and an arc (pizza slice):

6. Half of a circle:

H. Word Problems (Use π = 22/7):

1. A circular pond in a park has a diameter of 21 metres. What is the circumference of the pond?

2. Riya ties a rope to a pole and walks in a circle. The rope is 7 metres long. What is the diameter of the circle she makes? What is the circumference?

3. A circular clock face has a radius of 15 cm. What is the distance around the clock face?

4. The wheel of Dhruv's toy car has a diameter of 3.5 cm. How far does the car travel in 10 complete rotations of the wheel?

5. A circular field has a radius of 35 metres. A farmer walks along the boundary twice every morning. What is the total distance he walks?

Activity — Circle Art (Rangoli Design)

Create a beautiful rangoli design using concentric circles!

Materials Needed:

A compass
A pencil and eraser
Coloured pencils or sketch pens
A blank sheet of paper

Instructions:

Mark a point O in the centre of your paper.
Using your compass, draw a circle with radius 2 cm from point O.
Without moving the needle, draw another circle with radius 3 cm.
Continue drawing circles with radii 4 cm, 5 cm, 6 cm, and 7 cm.
You now have 6 concentric circles!
Colour each ring (the space between two circles) with a different colour to make a rangoli pattern.
You can also add flower petals or geometric patterns in each ring.

Measure and record:

Circle #	Radius (r)	Diameter (d = 2r)	Circumference (C = 2πr, use π = 22/7)
1	2 cm	4 cm	12.57 cm
2	3 cm	6 cm	18.86 cm
3	4 cm
4	5 cm
5	6 cm
6	7 cm

Observation: What do you notice about the circumference as the radius increases? (Answer: The circumference also increases. When radius doubles, circumference also doubles!)

Want to review the lesson again?

Mathematics

Circles — Radius, Diameter, Circumference

Class 5 | CBSE / NCERT / ICSE

Name: Class: Date:

Learning Objectives

Understand what a circle is and identify its parts
Learn the relationship: Diameter = 2 × Radius
Find circumference using C = πd = 2πr (π ≈ 22/7 or 3.14)
Draw circles with a compass and understand concentric circles
Solve word problems involving circles

Introduction — Circles All Around Us

Circles are everywhere! Wheels, coins (₹1, ₹2, ₹5), bangles, the Ashoka Chakra on our flag, clock faces, satellite dishes, manhole covers, Olympic rings — all are circles. A circle has no corners and no straight sides. It is a perfectly round shape. In this chapter we learn the parts of a circle, the special number π (pi), and how to find the distance around a circle.

[Image: Collage of real-life circles — coin, wheel, bangle, Ashoka Chakra, clock, satellite dish]

What is a Circle?

Definition: A circle is a closed curve where every point is at the same distance from a fixed point called the centre. A circle is NOT a polygon (no straight sides, no corners).

Parts of a Circle

[Image: Labelled diagram showing all parts of a circle — centre O, radius, diameter, chord, arc, circumference, semicircle, sector, segment]

Part	What It Is	Key Fact
Centre (O)	Fixed point inside the circle	All radii measured from here
Radius (r)	Line from centre to the boundary	All radii are equal; r = d/2
Diameter (d)	Line through centre, both ends on circle	d = 2r; longest chord
Chord	Line with both ends on circle	Diameter is longest chord
Arc	Part of the circumference	Minor (small) and Major (large)
Circumference	Distance around the circle	C = πd = 2πr
Semicircle	Half of a circle	Formed by a diameter
Sector	Region between 2 radii + arc	Pizza slice shape
Segment	Region between chord + arc	Minor and Major

Radius and Diameter Relationship

Golden Rule: Diameter = 2 × Radius (d = 2r) | Radius = Diameter ÷ 2 (r = d/2)

[Image: Circle showing radius and diameter with labels showing d = 2r relationship]

Examples — Finding Diameter from Radius:
• Radius = 7 cm → d = 2 × 7 = 14 cm
• Radius = 3.5 cm (bangle) → d = 2 × 3.5 = 7 cm
• Radius = 4.5 cm (Ashoka Chakra) → d = 2 × 4.5 = 9 cm

Examples — Finding Radius from Diameter:
• Diameter = 2.3 cm (₹5 coin) → r = 2.3 ÷ 2 = 1.15 cm
• Diameter = 28 m (garden) → r = 28 ÷ 2 = 14 m
• Diameter = 3.5 m (well) → r = 3.5 ÷ 2 = 1.75 m

Object	Radius	Diameter
₹1 coin	1.1 cm	2.2 cm
₹5 coin	1.15 cm	2.3 cm
Cricket ball	3.6 cm	7.2 cm
Bicycle wheel	34 cm	68 cm
Circular park	50 m	100 m

Circumference — Distance Around a Circle

Circumference = the total distance around a circle (like perimeter for a circle).

[Image: Ant walking around a circle — showing circumference as the distance the ant covers in one full loop]

Pi (π): A special constant ≈ 3.14 or 22/7. It is the ratio of circumference to diameter for ANY circle.
Formulas: C = π × d | C = 2 × π × r
Did You Know? Indian mathematician Aryabhata (476 AD, Patna) calculated π ≈ 3.1416!

Example 1: d = 14 cm → C = 22/7 × 14 = 44 cm
Example 2: r = 7 cm → C = 2 × 22/7 × 7 = 44 cm
Example 3: Garden, r = 21 m → C = 2 × 22/7 × 21 = 132 m (fencing needed)
Example 4: Bicycle wheel, d = 70 cm → C = 22/7 × 70 = 220 cm (distance per rotation)
Example 5: Circular track, d = 56 m → C = 22/7 × 56 = 176 m; 5 rounds = 880 m

Drawing Circles with a Compass

Step	What to Do
1	Decide the radius and open the compass to that measurement using a ruler.
2	Place the needle point firmly on the paper — this is the centre O.
3	Hold the top knob and rotate slowly until the pencil draws a complete circle.
4	Mark the centre with a dot and label it O.

Concentric Circles

Concentric circles = same centre, different radii (like a target board).

[Image: Concentric circles with same centre O and different radii. Real-life: archery target, Ashoka Chakra, tree rings, water ripples]

Real-life examples: Archery target, tree trunk rings, ripples in water, dartboard, CD tracks, rangoli patterns.

Example: Three concentric circles with radii 2 cm, 4 cm, 6 cm:
Diameters: 4 cm, 8 cm, 12 cm. All share the same centre.

Word Problems

Problem 1: Circular playground, d = 42 m. Boundary length?
C = 22/7 × 42 = 132 m

Problem 2: Circular table, r = 70 cm. Lace for edge?
C = 2 × 22/7 × 70 = 440 cm = 4.4 m

Problem 3: Well, d = 3.5 m. Circumference?
C = 22/7 × 3.5 = 11 m

Problem 4: Bullock cart wheel, r = 35 cm. Rotations for 440 m?
C = 2 × 22/7 × 35 = 220 cm = 2.2 m. Rotations = 440 ÷ 2.2 = 200

Problem 5: Circular rangoli, r = 1.4 m. Edge length?
C = 2 × 22/7 × 1.4 = 8.8 m

Key Words

Term	Meaning
Circle	Closed curve, every point equidistant from centre
Centre (O)	Fixed point inside the circle
Radius (r)	Distance from centre to circle; r = d/2
Diameter (d)	Line through centre, both ends on circle; d = 2r
Chord	Line with both ends on circle
Circumference (C)	Distance around the circle; C = πd = 2πr
Pi (π)	≈ 3.14 or 22/7; same for all circles
Semicircle	Half of a circle
Sector	Pizza-slice region (2 radii + arc)
Concentric	Same centre, different radii

Key Points to Remember:
• A circle is NOT a polygon — no sides, no vertices, no angles.
• d = 2r and r = d/2. Diameter is the longest chord.
• Circumference = πd = 2πr where π ≈ 3.14 or 22/7.
• π is the same for ALL circles (ratio of circumference to diameter).
• Aryabhata (India, 5th century) calculated π ≈ 3.1416.
• A circle has infinite lines of symmetry.
• One wheel rotation covers a distance = circumference.
• Concentric circles: same centre, different radii.

Practice Questions

A. Fill in the Blanks:

1. A circle is a closed curve where every point is at the same distance from the .

2. The distance from the centre to any point on the circle is called the .

3. Diameter = × Radius.

4. The longest chord of a circle is the .

5. The total distance around a circle is called the .

6. π is approximately equal to or .

7. Half of a circle is called a .

8. Circles with the same centre but different radii are called circles.

9. A circle has lines of symmetry.

10. The Indian mathematician calculated π in the 5th century.

B. Find the Diameter (given Radius):

1. r = 6 cm → d =

2. r = 9.5 cm → d =

3. r = 14 m → d =

4. r = 3.5 m → d =

5. r = 21 cm → d =

C. Find the Radius (given Diameter):

1. d = 18 cm → r =

2. d = 7 m → r =

3. d = 44 cm → r =

4. d = 5.6 m → r =

5. d = 100 cm → r =

D. Find the Circumference (Use π = 22/7):

1. d = 14 cm → C =

2. r = 7 m → C =

3. d = 28 cm → C =

4. r = 21 m → C =

5. d = 35 cm → C =

E. True or False:

1. A circle is a polygon.

2. The diameter is the longest chord of a circle.

3. All radii of a circle are equal.

4. A chord always passes through the centre.

5. π is exactly equal to 3.14.

6. A semicircle is half of a circle.

7. The diameter is always twice the radius.

8. Concentric circles have the same radius.

F. Choose the Correct Answer (MCQ):

1. The radius of a circle is 10 cm. What is the diameter?

a) 5 cm b) 10 cm c) 20 cm d) 40 cm

2. The value of π is approximately:

a) 3.41 b) 3.14 c) 2.14 d) 4.14

3. Which is the longest chord of a circle?

a) Radius b) Arc c) Diameter d) Sector

4. If diameter = 7 cm, circumference = (π = 22/7):

a) 44 cm b) 22 cm c) 14 cm d) 11 cm

5. How many lines of symmetry does a circle have?

a) 1 b) 4 c) 8 d) Infinite

G. Name the Parts of a Circle:

1. Line from centre to boundary:

2. Line through centre, both ends on circle:

3. Line with both ends on circle (not through centre):

4. Distance around the circle:

5. Pizza-slice region (2 radii + arc):

6. Half of a circle:

H. Word Problems (Use π = 22/7):

1. A circular pond has diameter 21 m. Find its circumference.

2. Riya ties a 7 m rope to a pole and walks in a circle. Find the diameter and circumference.

3. A clock face has radius 15 cm. Find the distance around it. (Use π = 3.14)

4. Toy car wheel diameter = 3.5 cm. Distance in 10 rotations?

5. Circular field, r = 35 m. Farmer walks the boundary twice. Total distance?

Activity — Circle Art (Rangoli Design)

Draw 6 concentric circles with radii 2, 3, 4, 5, 6, 7 cm using a compass. Colour each ring differently. Then complete the table:

Circle #	Radius (r)	Diameter (d = 2r)	Circumference (C = 2πr)
1	2 cm	4 cm	12.57 cm
2	3 cm	6 cm	18.86 cm
3	4 cm
4	5 cm
5	6 cm
6	7 cm

Observation: What happens to circumference when radius increases?

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