Mensuration Formula

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!

Source: toppr.com

Mensuration Formula

What is Mensuration?

Mensuration is useful about the measurement of shapes and figures. It is applicable with 2-D and 3-D 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 2-D 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 3-D shape. These are having depth, breadth, and length.

Formulas of Mensuration

1. Area of Square:

A = a²

A	Area
a	side

2. Perimeter of Square:

P = 4 × a

P	Perimeter
a	side

3. Perimeter of the Rectangle:

P= 2 × ( L+B)

Where,

P	Perimeter
L	Length
B	Breadth

4. Area of the rectangle:

A= L× B

A	Area
L	Length
B	Breadth

5. Surface area of a cube:

S = 6 × A²

Where,

S	The surface area of a cube
A	Length of the side of a cube

6. Surface Area of a Cuboid:

S =2 × (LB + BH + HL)

Where,

S	Surface Area of Cuboid
L	Length of Cuboid
B	Breadth of Cuboid
H	Height of Cuboid

7. Surface Area of a Cylinder:

S= 2 × π × R × (R+H)

Where,

S	Surface Area of Cylinder
R	The radius of Circular Base
H	Height of Cylinder

8. Surface Area of a Sphere:

S =4 × π × R²

Where,

S	Surface Area of Sphere
R	Radius of Sphere

9. Surface Area of a Right circular cone:

S = π × r(l+r)

Where,

S	Surface Area of Cone
R	The radius of Circular Base
L	Slant Height of Cone

 

10. Volume of a cube:

V = A³

Where,

V	Volume of cube
A	side of cube

11. Volume of Cuboid:

V = L × B × H

V	Volume of Cuboid
L	Length of Cuboid
B	Breadth of Cuboid
H	Height of Cuboid

12. Volume of a Cylinder:

V= π × R² × H

Where,

V	Volume of Cylinder
R	The radius of Circular Base
H	Height of Cylinder

13. Volume of a Right circular cone:

V = ( π × R² × H ) ÷ 3

Where,

V	Volume of Cone
R	The radius of Circular Base
H	Height of Cone

14. Volume of a Sphere:

V = \(\frac{4}{3}\) × π × R³

Where,

V	Volume of Sphere
R	Radius of Sphere

15. Volume of a Right circular cone:

V = \(\frac{1}{3}\) × π × R² × 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 = π × R² × H

i.e. h =\(\frac{V}{π × R²}\)

=\(\frac{154000}{15400}\)

= 10 cm

Therefore, height of the cylinder will be 10 cm.