Unit of Volume is cubic meter represented as m^{3}. Volume is a measure of the capacity of any vessel or a three-dimensional body. In the International System of Units (SI), the unit of volume is m^{3}. Volume can also be represented in other units such as cubic centimetres, litres, millilitres, gallons, etc.
In this article, we will learn the definition of volume, its unit in various systems, some solved examples, and frequently asked questions related to the unit of volume.
What is Volume?
Volume is the measure of the amount of space that a three-dimensional body can fill or occupy. For vessels, it is called as the capacity of the vessel. The definition of volume is written as follows,
Volume is the space occupied by a three-dimensional solid body.
Volume Formula
Formula of volume is different for different shapes. Some common formulas of volume for distinct shapes are given below:
Shape |
Volume Formula |
---|---|
Cube |
a^{3} |
Cuboid |
l Ã— b Ã— h |
Cylinder |
Ï€r^{2}h |
Sphere |
4/3Ï€r^{3} |
Cone |
1/3Ï€r^{2}h |
Read More, Volume Formulas for 3D Shapes
What is Unit of Volume?
Unit of Volume is the measurement of the amount of fluid or space in a container. Unit of any physical quantity refers to a standard amount of the quantity chosen so that further measurements can be expressed relative to this quantity.
Unit of volume depends directly on the unit of length chosen while calculating volume of three-dimensional bodies. As SI unit of length is metre (m), the SI unit of volume becomes cubic metre (m^{3}).
While defining capacity of vessels in litres or gallons, we use the relation that 1000 litre capacity equals to the space occupied by a cube having side length equal to 1 m. In other words, 1000 litre = 1 cubic metre of the volume.
Dimensional Formula for Volume
There are different formula for calculating volume of different three-dimensional shapes, but dimensional formula of any physical quantity remains same irrespective if the formulae available to find value of the quantity.
Therefore, let us find the dimensional formula for volume by using the formula to find volume of a cube.
Volume of a cube, V = a^{3}, where a is the length of side of the cube.
We have the dimensional formula for side length as [M^{0 }L^{1 }T^{0}]. Thus, dimensional formula for volume would be found as follows,
Dimensional Formula of Volume = [M^{0} L^{1} T^{0}]^{3} = [M^{0} L^{3} T^{0}]
Dimensional Formula of Volume = [M^{0} L^{3} T^{0}]
What is 1 cubic metre?
1 cubic metre is the SI unit of volume abbreviated as 1 m^{3}. It represents the volume of a cube having side length equal to 1 metre.
SI unit of Volume
S.I. unit of volume is cubic metre abbreviated as m^{3}. It is so because S.I. unit of length is metre and volume involves cube of length in its formula as a fundamental unit. Thus, it is derived as follows,
- S.I. unit of length = metre
We have,
Volume of a Cube = (Length of Side)^{3}
S.I. unit of Volume = (S.I. unit of Length)^{3}
S.I. unit of Volume = (metre)^{3} = m^{3}
Thus, we obtain SI unit of volume = cubic metre or m^{3}.
Other Units of Volume
Unit is a standard measurement of any physical quantity. The unit of volume in different systems is mentioned below:
System |
Unit |
---|---|
MKS system |
metre^{3} or m^{3}, liters (l) |
CGS system |
centimetre^{3} or cm^{3} |
Imperial system |
pints, gallons |
Others |
barrels, bushels |
The units such as liters, pints, gallons, and barrels are used to express the capacity of vessels, i.e. the amount of a fluid they can hold whereas units such as cubic metre and cubic centimeter represent the volume of solids in relation to their dimensions.
The SI unit of volume can be adjusted to different measures by applying some prefixes as shown in the table below:
Unit of Volume |
Symbol |
Equivalent in m^{3} |
---|---|---|
cubic millimetre |
mm^{3} |
10^{-9} |
cubic centimetre |
cm^{3} |
10^{-6} |
cubic decimetre |
dm^{3} |
10^{-3} |
cubic metre |
m^{3} |
1 |
cubic decametre |
dam^{3} |
10^{3} |
cubic hectometre |
hm^{3} |
10^{6} |
cubic kilometre |
km^{3} |
10^{9} |
Conversion Between Unit of Volume
Unit of volume can be converted from one system to another using the conversion factors given in the following table:
Unit |
cubic metre |
litres |
---|---|---|
cubic metre |
1 |
1000 |
cubic centimetre |
0.000001 |
0.001 |
litres |
0.001 |
1 |
pints |
0.000473 |
0.473 |
gallons |
0.003785 |
3.785 |
barrels |
0.158988 |
158.988 |
bushels |
0.035239 |
35.23906 |
cubic inch |
0.000016 |
0.01638 |
cubic foot |
0.028316 |
28.3168 |
cubic decimeter |
0.001 |
1 |
Solved Questions on Unit of Volume
Question 1: A cuboidal box has its length, breadth and height as 5 cm, 8 cm and 10 cm respectively. Calculate its volume in SI units.
Solution:
We have,
Length of cuboid = 5 cm
Breadth of cuboid = 8 cm
Height of cuboid = 10 cm
Also, Volume of cuboid = Length x Breadth x Height
Thus, Volume = 5 x 8 x 10 = 400 cm^{3}
Hence, we have obtained volume of the cuboid as 400 cm^{3} or 0.0004 m^{3} in SI units.
Question 2: A cubical vessel has a capacity of 1000 litres. Determine the side length of the cube.
Solution:
Here we have, Capacity of cube = 1000 litres = 1000 x 0.001 m^{3} = 1 m^{3}
Now, Capacity = Volume
For cube, Volume = (side)^{3}
Thus, (side)^{3} = 1 or side = 1 m
Hence, we obtained that side length of the cube having 1000 litres capacity is 1 metre (m).
Practice Questions on Unit of Volume
Question 1: Convert 1000 litres into cm^{3}.
Question 2: Convert 1 m^{3} into dam^{3}.
Question 3: How many litres are there in 2 barrels?
Question 4: Convert 20 litres into gallons.
Question 5: Convert 1000 cm^{3} into litres.
FAQs on Unit of Volume
What is Volume?
Volume is defined as the amount of three-dimensional space occupied by an object or substance. It is a measure of space an object takes up.
What is SI unit of volume?
The SI unit of volume is cubic metre abbreviated as m^{3}.
What is the difference between volume and capacity?
Volume and Capacity are related concepts , but they have distinct meanings. Volume is the amount of space an object occupies, while capacity relates to the maximum quantity of substance a container can hold.
What are some commonly used units of volume?
Commonly used units of volume are m^{3}, cm^{3}, litres, millilitres, etc.
How much is 1 m^{3}?
1 m^{3} is the volume of a cube having its side length as 1 metre. It can hold 1000 litres of a fluid.
What is unit of volume in British system?
In the British system, the most commonly used unit of volume is gallon. Other common units of volume in the British system include pints, quarts, and fluid ounces.