PPT: Mensuration | Quantitative Techniques for CLAT PDF Download

 Page 1


Mensuration
Page 2


Mensuration
Introduction
What is Mensuration?
Mensuration is a section of 
mathematics that 
communicates about the 
length, volume, or area of 
various geometric shapes. 
These shapes or patterns 
exist in two dimensions or 
three dimensions.
Why Study 
Mensuration?
Understanding mensuration 
helps us calculate 
measurements in our daily 
lives, from determining the 
amount of paint needed for a 
room to calculating the 
volume of water in a tank.
Applications
Mensuration finds 
applications in various fields 
including construction, 
engineering, architecture, 
interior design, and even 
cooking where precise 
measurements are crucial.
Page 3


Mensuration
Introduction
What is Mensuration?
Mensuration is a section of 
mathematics that 
communicates about the 
length, volume, or area of 
various geometric shapes. 
These shapes or patterns 
exist in two dimensions or 
three dimensions.
Why Study 
Mensuration?
Understanding mensuration 
helps us calculate 
measurements in our daily 
lives, from determining the 
amount of paint needed for a 
room to calculating the 
volume of water in a tank.
Applications
Mensuration finds 
applications in various fields 
including construction, 
engineering, architecture, 
interior design, and even 
cooking where precise 
measurements are crucial.
Mensuration 3D in Maths- Important 
Terminologies
Key Definitions
Let us discover a few more 
definitions linked to the various 
geometric shapes. 
Understanding these terms will 
help us better comprehend the 
properties and formulas of 3D 
shapes.
Knowing the terminology is 
essential for solving 
mensuration problems 
accurately and efficiently.
Properties of Cube
All sides are equal
The Cube has all six faces in 
a square shape
Each of the faces meets the 
other four faces
The edges opposite to each 
other are parallel
Cube Formulas
Side = a
Volume = a³
Surface area = 6a²
Diagonal = :3a
Page 4


Mensuration
Introduction
What is Mensuration?
Mensuration is a section of 
mathematics that 
communicates about the 
length, volume, or area of 
various geometric shapes. 
These shapes or patterns 
exist in two dimensions or 
three dimensions.
Why Study 
Mensuration?
Understanding mensuration 
helps us calculate 
measurements in our daily 
lives, from determining the 
amount of paint needed for a 
room to calculating the 
volume of water in a tank.
Applications
Mensuration finds 
applications in various fields 
including construction, 
engineering, architecture, 
interior design, and even 
cooking where precise 
measurements are crucial.
Mensuration 3D in Maths- Important 
Terminologies
Key Definitions
Let us discover a few more 
definitions linked to the various 
geometric shapes. 
Understanding these terms will 
help us better comprehend the 
properties and formulas of 3D 
shapes.
Knowing the terminology is 
essential for solving 
mensuration problems 
accurately and efficiently.
Properties of Cube
All sides are equal
The Cube has all six faces in 
a square shape
Each of the faces meets the 
other four faces
The edges opposite to each 
other are parallel
Cube Formulas
Side = a
Volume = a³
Surface area = 6a²
Diagonal = :3a
Properties of Cuboid
1
Three-Dimensional 
Features
A cuboid is a three-dimensional 
shape with length, breadth, and 
height. Unlike a cube, a cuboid's 
dimensions can differ, making it 
more versatile but requiring 
more complex formulas.
2
Dimensions
Height = h, Length = l and 
Breadth = b. These three 
parameters are essential for 
calculating all properties of a 
cuboid.
3
Key Formulas
Volume = l × b × h = Area of base 
× height
Surface area = 2(lb + bh + hl)
Diagonal = :(l²+b²+h²)
Area of four walls = Perimeter of 
base × height = 2(l + b)× h
Volume of metal = External 
volume 3 internal volume
Page 5


Mensuration
Introduction
What is Mensuration?
Mensuration is a section of 
mathematics that 
communicates about the 
length, volume, or area of 
various geometric shapes. 
These shapes or patterns 
exist in two dimensions or 
three dimensions.
Why Study 
Mensuration?
Understanding mensuration 
helps us calculate 
measurements in our daily 
lives, from determining the 
amount of paint needed for a 
room to calculating the 
volume of water in a tank.
Applications
Mensuration finds 
applications in various fields 
including construction, 
engineering, architecture, 
interior design, and even 
cooking where precise 
measurements are crucial.
Mensuration 3D in Maths- Important 
Terminologies
Key Definitions
Let us discover a few more 
definitions linked to the various 
geometric shapes. 
Understanding these terms will 
help us better comprehend the 
properties and formulas of 3D 
shapes.
Knowing the terminology is 
essential for solving 
mensuration problems 
accurately and efficiently.
Properties of Cube
All sides are equal
The Cube has all six faces in 
a square shape
Each of the faces meets the 
other four faces
The edges opposite to each 
other are parallel
Cube Formulas
Side = a
Volume = a³
Surface area = 6a²
Diagonal = :3a
Properties of Cuboid
1
Three-Dimensional 
Features
A cuboid is a three-dimensional 
shape with length, breadth, and 
height. Unlike a cube, a cuboid's 
dimensions can differ, making it 
more versatile but requiring 
more complex formulas.
2
Dimensions
Height = h, Length = l and 
Breadth = b. These three 
parameters are essential for 
calculating all properties of a 
cuboid.
3
Key Formulas
Volume = l × b × h = Area of base 
× height
Surface area = 2(lb + bh + hl)
Diagonal = :(l²+b²+h²)
Area of four walls = Perimeter of 
base × height = 2(l + b)× h
Volume of metal = External 
volume 3 internal volume
Properties of Cylinder
Structure
A cylinder has one 
curved side and two 
vertical flat ends in the 
circular shape. This 
unique structure gives 
cylinders their 
distinctive properties.
Volume Formula
Volume = Ãr²h, where 
r is the radius of the 
circular base and h is 
the height of the 
cylinder. This formula 
represents the total 
space contained 
within the cylinder.
Surface Area
Surface area = 2Ãrh 
(curved surface area)
T otal surface area = 
2Ãr(h + r), which 
includes both circular 
ends and the curved 
surface.