Volume of a Cube Formula

# Volume of a Cube Formula

## 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 cm3

Thus, the volume of the cube = 5 × 5 × 5 = 125 cm3

= (length × breadth × height) cm3

But in a cube length = breadth = height

Thus, the volume of the cube = (length × length × length) cm3

Or, Volume of a cube = (side × side × side) cm3

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

Volume of the cube = (side)3

= (9)3 cm3

= 729 cm3

Example 2: If the volume of a cube is 512 cm3, find the measure of each side of the cube.

Solution: We have, V = 512 cm3

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, d2 = l2 + l2 + l2

d2 = (15)2 + (15)2 + (15)2

d2 = 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 cm3 = (2)3 cm3 = 8 cm3

Volume of a cubical box = (side)3 cm3 = (20)3 cm3 = 8000 cm3

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

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