Mensuration in Maths  Formulas for 2D and 3D Shapes, Examples
Mensuration is a branch of mathematics concerned with the calculation of geometric figures and their parameters such as weight, volume, form, surface area, lateral surface area, and so on.
Let’s learn about all the mensuration formulas in maths.
Mensuration Meaning
Mensuration is the branch of mathematics that deals with the measurement of various geometric figures and shapes. This includes calculating areas, volumes, and perimeters of twodimensional shapes like squares, rectangles, circles, and triangles, as well as threedimensional figures like cubes, cylinders, spheres, and cones.
These shapes can exist in 2 ways:
 TwoDimensional Shapes – circle, triangle, square, etc.
 ThreeDimensional Shapes – cube, cuboid, cone, etc.
Difference Between 2D and 3D Shapes
2Dimensional vs 3Dimensional Shapes 


2D Shape  3D Shape 
Any shape is 2D if it is bound by three or more straight lines in a plane.  A shape is a threedimensional shape if there are several surfaces or planes around it. 
There is no height or depth in these shapes.  In contrast to 2D forms, these are sometimes known as solid shapes and have height or depth. 
These shapes just have length and width as their dimensions.  Since they have depth (or height), breadth, and length, they are referred to as threedimensional objects. 
We can calculate their perimeter and area.  Their volume, curved surface area, lateral surface area, or total surface area can all be calculated. 
Mensuration Terminologies
Here is the list of terms you will come across in mensuration class. We have provided the term, it’s abbreviation, unit and definition for easy understanding.
Terms  Abbreviation  Unit  Definition 

Area  A  m^{2} or cm^{2}  The surface that the closed form covers is known as the area. 
Perimeter  P  cm or m  A perimeter is the length of the continuous line that encircles the specified figure. 
Volume  V  cm^{3} or m^{3}  A 3D shape’s space is referred to as its volume. 
Curved Surface Area  CSA  m^{2} or cm^{2}  The overall area is known as a Curved surface area if there is a curved surface. Example: Sphere 
Lateral Surface area  LSA  m^{2} or cm^{2}  The term “Lateral Surface area” refers to the combined area of all lateral surfaces that encircle the provided figure. 
Total Surface Area  TSA  m^{2} or cm^{2}  The total surface area is the total of all the curved and lateral surface areas. 
Square Unit  –  m^{2} or cm^{2}  A square unit is the area that a square of side one unit covers. 
Cube Unit  –  m^{3} or cm^{3}  The space taken up by a cube with a single side. 
Mensuration Formula For 2D Shapes
The following table provides a list of all mensuration formulas for 2D shapes:
Shape  Area (Square units)  Perimeter (units)  Figure 

Square  a^{2}  4a  
Rectangle  l × b  2 (l + b)  
Circle  πr^{2}  2 π r  
Scalene Triangle  √[s(s−a)(s−b)(s−c)], Where, s = (a+b+c)/2 
a+b+c  
Isosceles Triangle  ½ × b × h  2a + b  
Equilateral Triangle  (√3/4) × a^{2}  3a  
Right Angle Triangle  ½ × b × h  
Rhombus  ½ × d1 × d2  4 × side  
Parallelograms  b × h  2(l+b)  
Trapezium  ½ h(a+c)  a+b+c+d 
Learn More:
 Area of Trapezium
 Area of Polygons
 Area of General Quadrilateral
 Heron’s Formula
 Applications of Heron’s Formula
 Area of 2D Shapes
 Perimeter of circular figures
 Areas of sector and segment of a circle
 Areas of combination of plane figures
Mensuration Formula for 3D Shapes
The following table provides a list of all mensuration formulas for 3D shapes:
Shape  Volume (Cubic units)  Curved Surface Area (CSA) or Lateral Surface Area (LSA) (Square units)  Total Surface Area (TSA) (Square units)  Figure 
Cube  a^{3}  LSA = 4 a^{2}  6 a^{2}  
Cuboids  l × b × h  LSA = 2h(l + b)  2 (lb +bh +hl)  
Sphere  (4/3) π r^{3}  4 π r^{2}  4 π r^{2}  
Hemisphere  (⅔) π r^{3}  2 π r^{2}  3 π r^{2}  
Cylinder  π r ^{2} h  2π r h  2πrh + 2πr^{2}  
Cone  (⅓) π r^{2} h  π r l  πr (r + l) 
Learn More :
 Surface Area of Cube, Cuboid, and Cylinder
 Volume of Cube, Cuboid, and Cylinder
 Volume and Capacity
 Surface Area of 3D Shapes
 Volumes of Cubes and Cuboids
 Surface Areas and Volumes
 Volumes of a combination of solids
 Conversion of solids
 Frustum of a Cone
 Section of a Cone
 Conic Section
 Parabola
 Ellipse
 Hyperbola
Solved Problems on Mensuration
Let’s solve some example problems on mensuration.
Problem 1: Find the volume of a cone if the radius of its base is 1.5 cm and its perpendicular height is 5 cm.
Solution:
Radius of the cone, r = 1.5 cm
Height of the cone, h = 5 cm
∴ Volume of the cone, V = 13πr^{2}h=13×227×(1.5)^{2}×5= 11.79 cm^{3}
Thus, the volume of the cone is 11.79 cm^{3}.
Problem 2: The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone of height 24 cm is made. Find the radius of its base.
Solution:
The dimensions of the cuboid are 44 cm, 21 cm and 12 cm.
Let the radius of the cone be r cm.
Height of the cone, h = 24 cm
It is given that cuboid is melted to form a cone.
∴ Volume of metal in cone = Volume of metal in cuboid
⇒(1/3)πr^{2}h=44×21×12
(Volume of cuboid=Length×Breadth×Height)
⇒(1/3)×(22/7)×r^{2}×24=44×21×12
⇒r= √(44×21×12×21) / (22×24)
=21 cm
Thus, the radius of the base of cone is 21 cm.
Problem 3: The radii of two circular ends of frustum shape bucket are 14 cm and 7 cm. The height of the bucket is 30 cm. How many liters of water can it hold? (1 litre = 1000 cm^{3}).
Solution:
Radius of one circular end, r1 = 14 cm
Radius of other circular end, r2 = 7 cm
Height of the bucket, h = 30 cm
∴ Volume of water in the bucket = Volume of frustum of cone
=(1/3)πh(r_{1}^{2}+r_{1}r_{2}+r_{2}^{2})=13×22/7×30×(142+14×7+72)
=13×22/7×30×343=10780 cm^{3}
=107801000=10.780 L
Thus, the bucket can hold 10.780 litres of water.
FAQs On Mensuration
What is Mensuration?
Mensuration deals with the calculation of geometric figures and their parameters such as weight, volume, form, surface area, lateral surface area, and so on.
What are 2D and 3D Shapes?
Any shape is considered to be 2D if it is bound by three or more straight lines in a plane whereas a shape is a threedimensional shape if there are several surfaces or planes around it.
What is Area of Cylinder Formula?
Lateral or Curved Surface area of a cylinder = 2π r h
Total Surface Area of a cylinder = 2πrh + 2πr^{2}
What is TSA (Total Surface Area) of Sphere Formula?
Area of Sphere is given by the following formula :
A= 4 π r^{2}
What is Volume of Cone Formula?
Volume of Cone is given by the following formula :
V= (⅓) π r^{2} h
What is Area of Triangle Formula?
Area of Triangle is given by the following formula :
A= 1/2 ×b ×h
What is Area of Circle Formula?
Area of Circle is given by the following formula :
A= π r^{2}
What is Volume of Cylinder Formula?
Volume of Cylinder is given by the following formula :
V= π r ^{2} h