Circles (Grade 4)
A circle is a round, closed shape where every point on the boundary is the same distance from the centre. Coins, bangles, wheels, and clock faces are all circles.
In Class 4, you will learn the parts of a circle — centre, radius, diameter, and circumference — and how they are related.
What is Circles - Class 4 Maths (Geometry)?
A circle is a closed curve where every point on the curve is at an equal distance from a fixed point called the centre.
The key parts of a circle are:
- Centre: The fixed point in the middle of the circle.
- Radius (r): The distance from the centre to any point on the circle.
- Diameter (d): The distance across the circle through the centre. It is the longest line segment inside a circle.
- Circumference: The boundary (perimeter) of the circle — the distance around it.
- Chord: A line segment joining any two points on the circle. The diameter is the longest chord.
Circles (Grade 4) Formula
Diameter = 2 × Radius | Radius = Diameter ÷ 2
If the radius of a circle is 5 cm, the diameter is 2 × 5 = 10 cm.
If the diameter is 14 cm, the radius is 14 ÷ 2 = 7 cm.
Types and Properties
Drawing a circle:
To draw a circle, use a compass:
- Open the compass to the desired radius using a ruler.
- Place the pointed end on the paper — this is the centre.
- Rotate the pencil end all the way around to complete the circle.
Concentric circles are circles that share the same centre but have different radii. Think of a dartboard or the rings on a tree trunk.
Solved Examples
Example 1: Example 1: Finding the diameter
Problem: The radius of a circle is 8 cm. Find the diameter.
Solution:
Step 1: Diameter = 2 × Radius
Step 2: Diameter = 2 × 8 = 16 cm
Answer: The diameter is 16 cm.
Example 2: Example 2: Finding the radius
Problem: The diameter of a bangle is 7 cm. Find its radius.
Solution:
Step 1: Radius = Diameter ÷ 2
Step 2: Radius = 7 ÷ 2 = 3.5 cm
Answer: The radius is 3.5 cm.
Example 3: Example 3: Circle parts on a coin
Problem: A ₹5 coin has a diameter of about 23 mm. What is its radius?
Solution:
Step 1: Radius = Diameter ÷ 2 = 23 ÷ 2 = 11.5 mm
Answer: The radius of the coin is 11.5 mm.
Example 4: Example 4: Identifying parts
Problem: In a circle, a line segment goes from one point on the circle to another point on the circle, passing through the centre. What is this line called?
Solution:
Step 1: It starts on the circle, passes through the centre, and ends on the circle.
Step 2: This matches the definition of a diameter.
Answer: It is the diameter.
Example 5: Example 5: Chord vs diameter
Problem: Dev draws a line from point A to point B on a circle. The line does not pass through the centre. What is this line called?
Solution:
Step 1: A line joining two points on a circle is a chord.
Step 2: Since it does not pass through the centre, it is a chord but NOT the diameter.
Answer: It is a chord. (The diameter is the longest possible chord.)
Example 6: Example 6: Drawing a circle with compass
Problem: Aditi wants to draw a circle with a radius of 4 cm. Describe the steps.
Solution:
Step 1: Open the compass to 4 cm using a ruler.
Step 2: Place the pointed end on the paper and mark a dot — this is the centre.
Step 3: Hold the pointed end steady. Rotate the pencil end all the way around.
Answer: A circle with radius 4 cm is drawn. Its diameter is 8 cm.
Example 7: Example 7: Concentric circles
Problem: Priya draws two circles with the same centre. One has radius 3 cm and the other has radius 5 cm. What are these called?
Solution:
Step 1: Both circles share the same centre.
Step 2: They have different radii (3 cm and 5 cm).
Answer: These are concentric circles.
Example 8: Example 8: Number of radii
Problem: How many radii can you draw in a circle?
Solution:
Step 1: A radius connects the centre to any point on the circle.
Step 2: There are infinitely many points on a circle.
Answer: You can draw infinitely many (unlimited) radii. All of them have the same length.
Example 9: Example 9: Diameter from radius in word problem
Problem: A circular garden has a radius of 15 m. Aman wants to walk straight across the garden through the centre. What distance will he cover?
Solution:
Step 1: Walking across the garden through the centre = diameter.
Step 2: Diameter = 2 × 15 = 30 m.
Answer: Aman will walk 30 m.
Real-World Applications
Circles are found everywhere in our world:
- Wheels — bicycles, cars, and auto-rickshaws roll on circular wheels.
- Coins — most Indian coins are circular.
- Clocks — the clock face is a circle.
- Bangles and rings — jewellery items are often circular.
- Plates and rotis — round shapes in cooking and eating.
Key Points to Remember
- A circle is a closed curve where every point is equally distant from the centre.
- Radius: distance from centre to circle. All radii are equal.
- Diameter: distance across the circle through the centre. Diameter = 2 × Radius.
- Chord: a line segment joining two points on the circle. Diameter is the longest chord.
- Circumference: the boundary (perimeter) of the circle.
- Use a compass to draw circles accurately.
- Concentric circles share the same centre but have different radii.
Practice Problems
- The radius of a circle is 12 cm. Find its diameter.
- The diameter of a circular plate is 26 cm. Find its radius.
- Draw a circle with radius 5 cm using a compass. Mark the centre, one radius, and one diameter.
- A wheel has a diameter of 70 cm. What is its radius in cm?
- Is the diameter of a circle always longer than any other chord? Explain why.
- Meera draws two concentric circles with radii 4 cm and 7 cm. What is the difference between their diameters?
- Name three circular objects in your classroom.
Frequently Asked Questions
Q1. What is the difference between radius and diameter?
The radius is the distance from the centre to the edge of the circle. The diameter goes all the way across through the centre. Diameter = 2 × Radius.
Q2. What is a chord?
A chord is a straight line segment joining any two points on the circle. The diameter is a special chord that passes through the centre and is the longest possible chord.
Q3. How many diameters can a circle have?
A circle can have infinitely many diameters. All diameters pass through the centre and all have the same length.
Q4. What is the circumference of a circle?
The circumference is the total distance around the circle — its perimeter. In higher classes, you will learn to calculate it using the formula C = 2 × pi × r.
Q5. What are concentric circles?
Concentric circles are two or more circles that share the same centre but have different radii. A dartboard is an example of concentric circles.
Q6. Is a circle a polygon?
No. A polygon has straight sides (like a triangle or rectangle). A circle has a curved boundary with no straight sides or corners.
Q7. How do you draw a circle without a compass?
You can trace around a circular object like a coin, a bangle, or the bottom of a glass. For accurate drawings in maths, a compass is recommended.
Q8. What is the longest line you can draw inside a circle?
The diameter is the longest line segment that fits inside a circle. Any other chord is shorter than the diameter.
