Formula for Volume of Cube – Derivation and Examples

Here you will learn what is the formula for volume of cube, its derivation and examples based on it.

Let’s begin – 

Formula for Volume of Cube

Let the side or edge of the cube be a,

Then the Volume of Cube = side \(\times\) side \(\times\) side = \(a^3\)

Also Read : Formula for Surface Area of Cube – Derivation & Examples

Derivation :

Since a cuboid, whose length, breadth and the height are all equal, is called a cube.

If each edge or side of the cube is s, then the Volume of cube would be (s × s × s), i.e., \(s^3\).

So, if a cube has side of 12 cm,

then volume of cube = 12 × 12 × 12 \(cm^3\)

= 1728 \(cm^3\)

Note : If an object is solid, then space occupied by such an object is measured, and is termed as the Volume of the object. On the other hand, if the object is hollow, then interior of the object is empty, and can be filled with air, or some liquid that will take the shape of its container.

Example : A child playing with building blocks, which are of the shape of cubes has built a structure with 15 cubes. If the edge of each cube is 3 cm, find the volume of the structure built by the child. 

Solution : Here, edge or side = 3cm

Volume of each cube = side × side × side

= 3 \(\times\) 3 \(\times\) 3 \(cm^3\) = 27 \(cm^3\)

Number of cubes in structure = 15

Therefore, volume of the structure = 27 \(\times\) 15 \(cm^3\)

= 405 \(cm^3\)

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