**Volume of a Cube**

The volume of a 3D shape is the measure of the space occupied by
that 3D shape. If the 3D shape is solid, the space occupied by it is called its
volume. If the 3D shape is hollow, then its interior can be filled by another
solid, gas or liquid. In that case, the volume is called the capacity of the
object.

The unit of volume (or capacity) is given in cubic units.

Let us take 125 cubes of side 1 cm each and arrange them as shown in the following figure.

We observe that the length of the cube
so formed is 5 cm.

So, 5 × 5 × 5 = 125

Volume of 125 cubes of side 1 cm = 125
× (1 × 1 × 1) = 125 cm^{3}

Thus, the volume of the cube = 5 × 5 ×
5 = 125 cm^{3}

= (length × breadth
× height) cm^{3}

But in a cube length = breadth =
height

Thus, the volume of the cube = (length
× length × length) cm^{3 }

Or, Volume of a cube = (side × side × side)
cm^{3 }

Therefore, **Volume of a cube = (side) ^{3}**

**Volume of a Cube
Formula**

**Volume of a cube = (side) ^{3}**

**Volume of a Cube
Example**

**Example 1:** Find the volume of a cube whose each
side measures 9 cm.

**Solution:** Here, side = 9
cm

^{3}

= (9)^{3}
cm^{3}

= 729 cm^{3}

**Example 2:** If the volume of
a cube is 512 cm^{3}, find the measure of each side of the cube.

**Solution:** We have, V = 512
cm^{3}

We know that, Volume of a cube = (side)^{3}

512 = (side)^{3}

8 × 8 × 8 = (side)^{3}

side = 8 cm

Hence, the side of the cube is 8 cm.

**Example 3:** Find
the diagonal of a cube, if its side measures 15 cm.

**Solution: **Given,
side = 15 cm

We know that, *d*^{2} = *l*^{2}
+ *l*^{2} + *l*^{2}

d^{2} = (15)^{2} + (15)^{2}
+ (15)^{2}

*d*^{2}
= 225 + 225 + 225 = 675

*d *= √675 cm =
15√3 cm

The length of the diagonal of the cube is 15√3 cm.

**Example 4: **How
many dice of side 2 cm can be put inside a cubical box of side 20 cm.

**Solution: **Given:
Side of the dice = 2 cm and side of the cubical box = 20 cm

Volume of a die = (side)^{3} cm^{3}
= (2)^{3} cm^{3 }= 8 cm^{3}

Volume of a cubical box = (side)^{3}
cm^{3} = (20)^{3} cm^{3 }= 8000 cm^{3}

Number of dice that can be put inside the cubical
box = 8000/8 = 1000

Hence, 1000 dice can be put inside the cubical box.