Mensuration is an interesting branch of mathematics. It studies the measurement of the geometrical figures and shapes like cube, cuboid, cone, sphere, cylinder, etc. We can measure various terms like surface area, volume, perimeter, etc. This article will help to learn and understand various Mensuration Formula with examples. Let us begin!
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Mensuration Formula
What is Mensuration?
Mensuration is useful about the measurement of shapes and figures. It is applicable with 2D and 3D geometrical shapes both. Using a specific mensuration formula from the many, we will able to solve the mensuration problems easily. So let us see these concepts of mensuration and their formulas.
If a shape is surrounded by three or more straight lines in a plane surface, then it is a 2D shape. And such shapes are having only length and breadth. If a shape is surrounded by a no. of surfaces or planes then it is termed as 3D shape. These are having depth, breadth, and length.
Formulas of Mensuration

Area of Square:
A = a^{2}
A  Area 
a  side 

Perimeter of Square:
P = 4 Ã— a
P  Perimeter 
a  side 

Perimeter of the Rectangle:
P= 2 Ã— ( L+B)
Where,
P  Perimeter 
L  Length 
B  Breadth 

Area of the rectangle:
A= LÃ— B
A  Area 
L  Length 
B  Breadth 

Surface area of a cube:
S = 6 Ã— A^{2}
Where,
S  The surface area of a cube 
A  Length of the side of a cube 

Surface Area of a Cuboid:
S =2 Ã— (LB + BH + HL)
Where,
S  Surface Area of Cuboid 
L  Length of Cuboid 
B  Breadth of Cuboid 
H  Height of Cuboid 

Surface Area of a Cylinder:
S= 2 Ã—Â Ï€Â Ã— R Ã— (R+H)
Where,
S  Surface Area of Cylinder 
R  The radius of Circular Base 
H  Height of Cylinder 

Surface Area of a Sphere:
S =4Â Ã—Â Ï€Â Ã— R^{2}
Where,
S  Surface Area of Sphere 
R  Radius of Sphere 
 Surface Area of a Right circular cone:
S = Ï€Â Ã— r(l+r)
Where,
S  Surface Area of Cone 
R  The radius of Circular Base 
L  Slant Height of Cone 

Volume of a cube:
V = A^{3}
Where,
V  Volume of cube 
A  side of cube 

Volume of Cuboid:
V = L Ã— B Ã— H
V  Volume of Cuboid 
L  Length of Cuboid 
B  Breadth of Cuboid 
H  Height of Cuboid 

Volume of a Cylinder:
V=Â Ï€Â Ã— R^{2}Â Ã— H
Where,
V  Volume of Cylinder 
R  The radius of Circular Base 
H  Height of Cylinder 

Volume of a Right circular cone:
V = (Â Ï€Â Ã— R^{2}Â Ã— H )Â Ã· 3
Where,
V  Volume of Cone 
R  The radius of Circular Base 
H  Height of Cone 

Volume of a Sphere:
V = \(\frac{4}{3}\) Ã—Â Ï€Â Ã— R^{3}
Where,
V  Volume of Sphere 
R  Radius of Sphere 

Volume of a Right circular cone:
V = \(\frac{1}{3}\) Ã—Â Ï€Â Ã— R^{2Â }Ã— H
Where,
V  Volume of Cone 
R  The radius of Circular Base 
H  Height of Cone 
Solved Examples
Q.1: Find out the height of a cylinder with a circular base of radius 70 cm and volume 154000 cubic cm.
Solution: A given here,
r= 70 cm
V= 154000 cubic cm
Since formula is,
V = Ï€Â Ã— R^{2}Â Ã— H
i.e. h =\(\frac{V}{Ï€Â Ã— RÂ²}\)
=\(\frac{154000}{15400}\)
= 10 cm
Therefore, height of the cylinder will be 10 cm.
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