Maths - Circle concepts with perimeter, area

⭕ CIRCLE LEARNING LAB

Explore • Understand • Calculate • Practise

Interactive Mathematics Simulator

Learning Outcomes

• Understand the meaning of a circle.
• Identify centre, radius, diameter and circumference.
• Understand how to draw a circle.
• Derive the formulas for circumference and area.
• Calculate perimeter and area using radius.
• Solve numerical problems independently.

Explore the Topics

1. What is a Circle?

A circle is a closed plane figure consisting of all points in a plane that are at the same fixed distance from a fixed point.

Definition: The fixed point is called the centre, and the fixed distance is called the radius.

Examples in daily life

Clock face, bicycle wheel, coins, circular plates, bangles and roundabouts.

2. Important Parts of a Circle

• Centre: The fixed point inside a circle.
• Radius: Distance from centre to any point on the circle.
• Diameter: A straight line passing through the centre and joining two points on the circle.
• Circumference: The total boundary length of the circle.
• Chord: A line segment joining two points on the circle.

Diameter = 2 × Radius

Radius = Diameter ÷ 2

3. How to Draw a Circle

Required materials: Compass, pencil, ruler and paper.

1. Mark a point on the paper. Name it O.
2. Measure the required radius using a ruler.
3. Open the compass to the measured distance.
4. Place the compass needle at O.
5. Rotate the pencil arm completely around O.
6. A circle is formed.

Remember: Keep the compass opening unchanged while drawing the circle.

4. Derivation of Formulas

A. Perimeter or Circumference

The perimeter of a circle is called its circumference. It is the total length around the circular boundary.

For every circle, the ratio of circumference to diameter is a constant called pi.

π = Circumference ÷ Diameter

Therefore,

Circumference = π × Diameter

We know that diameter = 2 × radius.

C = 2 × π × r

B. Area of a Circle

Area is the amount of surface enclosed within the circular boundary.

Imagine cutting a circle into many small sectors and arranging them alternately to form an approximate rectangle.

The approximate rectangle has:

• Length = Half the circumference = πr
• Breadth = Radius = r

Area of rectangle = Length × Breadth

Area = πr × r

A = πr²

Important: Use π = 22/7 or 3.14 as specified in the question. The sector rearrangement gives an exact limiting derivation as the number of sectors increases.

Units

Circumference is measured in centimetres (cm).

Area is measured in square centimetres (cm²).

5. Interactive Circle Simulator

Select a radius and observe how the circle changes.

Select Radius (cm) 1 cm 2 cm 3 cm 4 cm 5 cm 6 cm 7 cm 8 cm 9 cm 10 cm

Circle with radius 3 cm

Selected radius = 3 cm

Perimeter / Circumference

Formula: C = 2 × π × r

Area of Circle

Formula: A = π × r × r

This simulator uses π = 3.14 and displays answers to two decimal places.

6. Student Assessment

Enter the correct perimeter and area for each given radius.

Student Name Class and Section

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