Circles: calculate area, circumference, radius and diameter

key notes :

Parts of a Circle

Center (O): The fixed point in the middle.

Radius (r): The distance from the center to any point on the circle.

Diameter (d): The longest chord, passing through the center. d=2rd = 2rd=2r

Circumference (C): The distance around the circle (its perimeter).

Formulas

1. Radius and Diameter

• d=2r
• r=d/2

2. Circumference (Perimeter of Circle)

• C=2πr or C=πd

3. Area of Circle A=πr²

• 👉 Here, take π≈3.14 or 22/7​.

Examples

Example 1: Find circumference

Radius = 7 cm

C=2πr=2×22/7×7=44 cm

Example 2: Find area

Radius = 10 cm

A=πr²=3.14×10²=314 cm²

Example 3: Find radius when diameter is given

Diameter = 14 m

r=d/2=14/2=7 m

Example 4: Find diameter from circumference

Circumference = 31.4 cm

C=πd  ⟹  d=C/π=31.4/3.14=10 

Important Points

Always check whether radius or diameter is given.

Use π=22/7 if radius/diameter is a multiple of 7.

Units:

• Circumference → cm, m, km (linear units)
• Area → cm², m², km² (square units)

Practice Questions

1. Find the circumference of a circle with radius 14 cm.
2. A circle has diameter 20 cm. Find its radius and area.
3. Find the area of a circle with radius 21 m (take π=22/7​).
4. The circumference of a circle is 44 cm. Find its diameter and radius.
5. A circular park has a radius of 35 m. Find its area and circumference.

Learn with an example

Let’s practice!🖊️