Theory:

Volume is a space occupied by any three-dimensional object. It is also a derived quantity that can be measured by measuring lengths.
The formula is written as,
 
Volume=Length×Breadth×Height=Surfacearea×Height
 
SI Unit
 
Volume=l×b×h
 
If the unit of volume is written in \(m\), then
 
\(Volume\) \(=\) \(metre\) \(×\) \(metre\) \(×\) \(metre\)
 
\(=\) \(cubic\ metre\) or \(m^3\)
 
Hence, the SI unit of volume is a \(cubic\) \(metre\) (or) \(m^3\).
The Volume of regularly shaped objects
The volume of regularly shaped figures can be calculated using the relevant formula. Some of them are tabulated below.
 
Shape
Three-dimensional figure
Volume
Cube
cubevolpngpng.png
side×side×sidea×a×a=a3
Cuboid
cuboidvolpngpng.png
length×breadth×heightl×b×h
Sphere
Simple_sphere_with_radii.svg
43×π×(radius)343πr3
Cylinder
5w282.png
π×(radius)2×heightπr2h
Solved examples
1. Calculate the volume of a cube having sides of \(10\ m\).

Sides, \(a\ = 10\ m\)
 
By substituting the known values on the formula of a cube, we get the following.
 
Volumeofacube=a3=10×10×10=1000m3
 
Therefore, the volume of a cube is \(1000\ m^3\).
 
2. What will be the volume of a cylinder having a \(2\ m\) radius and \(7\ cm\) height?

Radius, \(r\ = 2\ m\)

Height, \(h\ = 7\ m\)
 
Volumeofacylinder=π×r2×h=227×(2)2×7=88cm3
 
Therefore, the volume of a cylinder is \(1000\ cm^3\).
Reference:
https://upload.wikimedia.org/wikipedia/commons/d/df/Simple_sphere_with_radii.svg