Volume is a measure of the capacity of any vessel or a three-dimensional body. In the International System of Units (SI), the standard unit for volume is the cubic meter (m³). Volume can also be represented in other units such as cubic centimetres, litres, millilitres, gallons, etc. Here, we will learn about some more units of volume that are used to express volume.
What is Volume?
Volume is the amount of space an object or substance occupies. It's like measuring the "3D size" of something. You can find it by multiplying its length, width, and height.
Also Learn, System of Units
Volume Formula,
The formula for volume is different for different shapes. Some common formulas of volume for distinct shapes are given below:
Shape | Volume Formula |
|---|---|
Cube | a3 |
Cuboid | l × b × h |
Cylinder | πr2h |
Sphere | 4/3πr3 |
Cone | 1/3πr2h |
Read More, Volume Formulas for 3D Shapes
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 = a3, where a is the length of side of the cube.
We have the dimensional formula for side length as [M0 L1 T0]. Thus, dimensional formula for volume would be found as follows,
Dimensional Formula of Volume = [M0 L1 T0]3 = [M0 L3 T0]
Dimensional Formula of Volume = [M0 L3 T0]
What is Unit of Volume?
The unit of volume measures the amount of fluid or space that a container or object can hold. A unit of measurement is a standard quantity used to express other measurements relative to it.
The unit of volume depends on the unit of length used. Since the S.I unit of length is the meter (m), the S.I. unit of volume is the cubic meter (m³).
When we talk about the capacity of containers in liters or gallons, we use the relationship that 1 cubic meter (m³) is equivalent to 1000 liters. This means that the space occupied by a cube with a side length of 1 meter is equal to 1000 liters.
S.I. unit of Volume
The SI unit of volume is the cubic meter (m³). This is because the SI unit of length is the meter (m), and since volume is calculated by cubing the length (multiplying length × width × height), it is expressed as the cube of the meter.
S.I. unit of length = metre
This is derived as follows:
So, 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 = m3
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.
Unit is a standard measurement of any physical quantity. The unit of volume in different systems is mentioned below:
System | Unit |
|---|---|
MKS system | metre3 or m3, liters (l) |
CGS system | centimetre3 or cm3 |
Imperial system | pints, gallons |
Others | barrels, bushels |
The S.I. 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 m3 |
|---|---|---|
cubic kilometre | km3 | 1,000,000,000 m3 |
hectometre cubic | hm3 | 1,000,000 m3 |
decametre cubic | dam3 | 1,000 m3 |
cubic metre | m3 | 1 m3 |
cubic decimetre | dm3 | 0.001 m3 |
cubic centimetre | cm3 | 0.000001 m3 |
cubic millimetre | mm3 | 0.000000001 m3 |
CGS Unit of Volume
The CGS unit of volume is the litre (L), which is equivalent to 1000 cubic centimetres (cm³).
Here’s a conversion table for litres and cubic centimetres, which can help with quick volume measurements and conversions:
Unit | Conversion |
|---|---|
Cubic centimetre | 1 cubic centimetre = 0.001 litrez |
Litre | 1 litre= 1000 cubic centimetres |
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 Examples
Example 1: A cuboidal box has its length, breadth and height as 5 cm, 8 cm and 10 cm respectively. Calculate its volume in S.I. 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 cm3
Hence, we have obtained volume of the cuboid as 400 cm3 or 0.0004 m3 in SI units.
Example 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 m3 = 1 m3
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).
Example 3: A cubical vessel has a capacity of 1000 litres. Determine the side length of the cube.
Solution:
1 litre = 1000 cubic centimetres (cm³), so 1000 litres = 1,000,000 cm³.
Volume of the cube = Side³, so:
Side3=1,000,000cm3
Side= ∛1000,000 = 100 cm
So, the side length of the cube is 100 cm.
Example 4: A cylindrical tank has a volume of 1500 litres. Determine the height of the tank if the radius of the base is 50 cm.
Solution:
1 litre = 1000 cm³, so 1500 litres = 1,500,000 cm³.
Volume of a cylinder = πr²h, where r is the radius and h is the height.
π×(50)2×h=1,500,000
π×2500×h=1,500,000
h=1,500,000/ π×2500=1,500,000/ 7850≈190.99cm
So, the height of the tank is approximately 191 cm.
Practice Questions
Question 1: Convert 1000 litres into cm3.
Question 2: Convert 1 m3 into dam3.
Question 3: How many litres are there in 2 barrels?
Question 4: Convert 20 litres into gallons.
Question 5: Convert 1000 cm3 into litres.
Conclusion
The SI (International System of Units) unit for volume is the cubic meter (m³), while the CGS (centimeter-gram-second) system uses the cubic centimeter (cm³) as its unit of volume.