## Measurement: Volume of Cube and Cuboid - Part 1

#### Units of Volume (l, ml, cm^{3})

Volume can be measured in several units.

Some of the more common ones are:

Following is the relation between the units of volume:

Some of the more common ones are:

- cm
^{3}or cubic centimetres - millilitres
- litres

Following is the relation between the units of volume:

- 1 litre = 1000 ml
- 1 ml = 1 cm
^{3} - 1 litre = 1000 cm
^{3}

#### 1. What are cubes and cuboids?

#### 2. What is a cubic unit?

1 cubic unit is the amount of space that a unit cube occupies.

Or simply,

**1 cubic unit = the volume of a unit cube**

The object below is made of 6 unit cubes.

Its volume is 6 cubic units.

Here are some other solids that have the same volume (6 cubic units).

#### 3. What is 1 cm^{3}?

1 cm

^{3}= the volume of a cube of 1-cm sides

The object below is made of eight 1-cm

^{3}units.

Its volume is 8 cm

^{3}or 8 cubic centimetres.

Here are some other solids that have the same volume (8 cm

^{3}).

#### 4. What is the volume of the cuboid below?

Each layer in the cuboid above has

**4**×

**3**= 12 cubes

Since there are

**2**layers in the cuboid, there are

2 × 12 =

**24 cubes altogether**.

Each of the 24 cubes has a volume of

**1 cm**.

^{3}So, the volume of the cuboid is 24 × 1 cm

^{3}=

**24 cm**.

^{3}**Volume of a cuboid = length × breadth × height**

Applying this formula in the example above, we get:

Volume of the given cuboid

= 4 cm × 3 cm × 2 cm

Volume of the given cuboid

= 4 cm × 3 cm × 2 cm

**= 24 cm**^{3}#### 5. What is the volume of the cube below?

A cube is a cuboid with the same length, breadth and height.

**Volume of a cube**

= length × breadth × height

**= length × length × length**

Volume of the given cube

= 5 cm × 5 cm × 5 cm

= 5 cm × 5 cm × 5 cm

**= 125 cm**^{3}#### 6. Calculate the volume of a cuboid-shaped crate that measures 3 m by 2 m by 1.7 m.

Volume of the crate

= 3 m × 2 m × 1.7 m

= 10.2 m

^{3}

The volume of the crate is

**10.2 m**.

^{3}