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Home >> Circle >> Area of Circle >> Area of Circle
Before you study this concept, you are advised to read:
What is Circle ?
Formula for Area of Circle = π radius^{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 cm^{2}
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 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 cm^{2}
Find radius of circle when its area is given
Example 3: Area of circle is 314 cm^{2}, find its radius.( value of π = 3.14)
Solution: As given in the question:
Area of circle = 314 cm^{2}
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 r^{2}
Divide both sides by 3.14 and we get:
100 = r^{2}
Take squareroot 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 cm^{2}, find its diameter.(use value of π = 3.14)
Solution: As given in the question:
Area of circle = 78.5 cm^{2}
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 squareroot 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 3.5^{2}
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 cm^{2}

