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Home >> Circle >> Area of Circle >>

Area of Circle

Center of circle Radius of circle Diameter of circle Chords of circle Semi-circle
Circumference of circle Interior of circle Exterior of circle Sector of a Circle Segment of a Circle
Area of Circle Arc of Circle Properties of Circle

Before you study this concept, you are advice to read:

What is Circle ?

Formula for Area of Circle = π r 2

Find area of circle when radius is given

Example 1: Find area of circle, if radius is 7 cm
Solution: As given in the question:

Radius = 7 cm

Apply formula of Area of Circle:
Area of Circle = π r 2

Put the value of radius & π and we get:
= (22/7) X 7 2

Expand the above exponential form and we get:
= 22/7 X 7 X 7

Solve the expression and we get:
= 154

Hence, Area of Circle = 154 cm2


Find area of circle when diameter is given

Example 2: Find area of circle, if diameter is 14 cm
Solution: As given in the question:

Diameter = 14 cm

This question is solved in two part:

Part 1 : Find Radius of Circle
Part 2 : Find Area of Circle

Part 1 : Steps to find Radius of Circle :

Apply formula to calculate Radius of Circle:

Radius = diameter/2

Put the value of diameter and we get:
Radius = 14/2

Solve the division expression and we get:
= 7

Therefore, Radius = 7 cm


Part 2 : Steps to find Area of Circle :

Apply formula of Area of Circle:
Area of Circle = π r 2

Put the value of radius (calculated in Part 1) & π and we get:
= 22/7 X 72

Expand the above exponential form and we get:
= 22/7 X 7 X 7

Solve the expression and we get:
= 154

Hence, Area of Circle = 154 cm2


Find radius of circle when its area is given

Example 3: Area of circle is 314 cm2, find its radius.( value of π = 3.14)
Solution: As given in the question:

Area of circle = 314 cm2

Apply the formula of Area of Circle:
Area of Circle = π r 2

Put the value of area of circle & π and we get:
314 = 3.14 r2

Divide both sides by 3.14 and we get:
100 = r2

Take square-root on both sides and we get:
10 = r

Or we can write it as:
R = 10

Hence, radius of circle is 10 cm


Find diameter of circle when its area is given

Example 4: Area of circle is 78.5 cm2, find its diameter.(use value of π = 3.14)
Solution: As given in the question:

Area of circle = 78.5 cm2

This question is solved in two part:

Part 1 : Find Radius of Circle
Part 2 : Find Diameter of Circle

Part 1 : Steps to find Radius of circle :

Apply the formula of Area of Circle:
Area of Circle = π r 2

Put the value of π and area of circle and we get:
78.5 = 3.14 r 2

Divide both sides by 3.14 and we get:
25 = r 2

Take square-root on both sides and we get:
5 = r

Or we can write it as:
R = 5

Therefore, radius of circle is 5 cm

Part 2 : Steps to find diameter of circle :

Apply formula to calculate Diameter:
Diameter = 2 X Radius

Put value of radius (calculated in Part 1) and we get:
Diameter = 2 X 5

Solve the above multiplication expression and we get:
= 10

Hence, diameter of circle is 10 cm


Find area of circle when circumference is given

Example 5: Circumference of circle is 22 cm. Find Area of circle.
Solution: As given in the question:

Circumference of circle = 44cm

This question is solved in two part:

Part 1 : Find Radius of Circle
Part 2 : Find Area of Circle

Part 1 : Steps to find Radius of Circle :

Apply formula to calculate Circumference:
Circumference = 2 π r

Put the value of circumference & π and we get:
22 = 2 (22/7) (r)

Divide both side by 2 and we get
11 = (22/7) (r)

Multiply both sides with 7/22 and we get:
7/2 = r

Convert the fraction into decimal and we get
= 3.5

Therefore, radius of circle = 3.5 cm


Part 2 : Steps to find Area of Circle :

Apply formula of Area of Circle:
Area of Circle = π r 2

Put value of radius (as calculated in Part 1) & π ( as 3.14) and we get:
Area of Circle = 3.14 X 3.52

Expand the above exponential form and we get:
= 3.14 X 3.5 X 3.5

Solve the above multiplication process and we get:
= 38.5

Area of Circle= 38.5 cm2


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