3D Mensuration

Last Updated : 09 Sep, 2025

3D Mensuration is the branch of mathematics that deals with the measurement of three-dimensional geometric shapes, including their surface area, volume, lateral surface area, and other related parameters. Unlike 2D shapes (flat figures), 3D objects have length, width, and height (or depth), making them solid structures.

3D Shapes: Cube, Cuboid, Sphere, Cylinder, Cone, Pyramid, Prism, etc.

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
Volume	V	cm³ or m³	A 3D shape's space is referred to as its volume.
Curved Surface Area	CSA	m² or cm²	The overall area is known as a Curved surface area if there is a curved surface. Example: Sphere.
Lateral Surface area	LSA	m² or cm²	The term "Lateral Surface area" refers to the combined area of all lateral surfaces that encircle the provided figure.
Total Surface Area	TSA	m² or cm²	The total surface area is the total of all the curved and lateral surface areas.
Square Unit	-	m² or cm²	A square unit is the area that a square of side one unit covers.
Cube Unit	–	m³ or cm³	The space taken up by a cube with a single side.

Mensuration Formula for 3D Shapes

The following table provides a list of all mensuration formulas for 3D shapes:

Shape	Volume	Curved Surface Area or Lateral Surface Area	Total Surface Area	Figure
Cube	a³	LSA = 4 a²	6a²	cube dimensions
Cuboids	l × b × h	LSA = 2h(l + b)	2(lb +bh +hl)	cuboid dimensions
Sphere	(4/3)πr³	4πr²	4πr²	sphere dimensions
Hemisphere	(⅔)πr³	2πr²	3πr²	hemisphere dimensions
Cylinder	πr²h	2πrh	2πrh + 2πr²	cylinder dimensions
Cone	(⅓)πr²h	πrl	πr(r + l)	cone dimensions