**What is Volume?**

Volume is the amount of space taken by any 3D object

Given above is the image of cube.

The total space covered by the cube is known as the Volume of Cube

Volume of cube can be calculated using following formula**Volume = Length x Width x Height**

**Units of Volume**

Volume of any object is calculated in **cubic units**

For example, consider the below cube of following dimension

Length = 4 cm

Width = 2 cm

Height = 5 cm

We know that:

Volume of Cube = Length x Breadth x Height

Volume = 4 cm x 2 cm x 5 cm

Volume = (4 x 2 x 5) .cm . cm. cm

\mathtt{Volume\ =\ 40\ ( cm)^{3}}

Here the unit of volume is \mathtt{( cm)^{3}}

**Conclusion**

The unit of volume of any geometric figure whether it is cube, cylinder or any object, is in **cubic unit**

**Important Rule for unit of volume**

While calculating volume & unit of any object, keep one rule in mind. . . . .

The calculation of volume should be done with **measurement of same unit**

For Example, consider the below cube

Given:

Length = 5 meter

Width = 2 meter

Height = 300 cm

Observe that unit of height is in centimeter, while unit of Length & Width is in Meter.

The units given are** inconsistent**.

In order to calculate the volume, make all units consistent with all the data.

Convert 300 cm into meter

We know that:

1 cm = 1/100 meter

300 cm = 300/100 = 3 meter

Now the data is:

Length = 5 meter

Width = 2 meter

Height = 3 meter

All the data units is in meter, **hence the data is consistent**

Cube Volume = Length x Breadth x Height

Volume = 5 meter x 2 meter x 3 meter

Volume = \mathtt{30\ ( m)^{3}}

**Common used volume metric**

**(a) Liter**

Liter is one of the common used metric in Volume

Have you ever gone to the super market to buy soft drink.

You would have noticed different capacity of bottles available.

If you are buying soft drink for yourself you will purchase half liter bottle.

But if you are planning for house party, you will buy big 1 liter or 2 liter bottle.

So what is the Liter mentioned in the bottle?

It is the** unit for volume of liquid** present in the bottle.

Just like \mathtt{m^{3}} , \mathtt{cm^{3}} ; **Liter** is also the unit for volume of any object.

**Relationship between Liter & \mathtt{m^{3}} **

1 Liter = 0.001 \mathtt{m^{3}}

OR

1 \mathtt{m^{3}} = 1000 Liter

**Example Explanation**

Consider the below aquarium whose water is filled to the brim.

Find the volume of water filled in liters

Observe that the aquarium is in the form of cuboid

**Given**

Length = 0.6 meter

Width = 0.4 meter

Height = 0.1 meter

All the measurement units are in meter, hence the data is consistent

We know that;**Volume of cuboid = Length x Breadth x Height**

Volume = 0.6 x 0.4 x 0.1 x \mathtt{m^{3}}

Volume = 0.024 \mathtt{m^{3}}

We have learnt that:

1 \mathtt{m^{3}} = 1000 Liter

0.024 \mathtt{m^{3}} = 0.024 x 1000 liter = 24 liter

**Hence the volume of above aquarium is 24 liter **

**(b) Milliliters** (ml)

**Milliliter** is another volume metric which is widely used in daily life.

This unit is used when comparatively less amount of volume is required.

**For Example**

Juice tetra packs in the market are of 500 to 700 ml packings.

The school water bottles are also available in 300 to 800 milliliters

**Relationship between Liters and Milliliters**

**1 Liter = 1000 Milliliters**

**Units of Volume – Questions**

(01) Find the volume of below cube in liters

In cube, all sides are of equal measurement

i.e. Length = Breadth = Height = 0.3 meter

We know that;**Volume of cube = Length x Breadth x Height**

Volume = 0.3 x 0.3 x 0.3 \mathtt{m^{3}}

Volume = 0.027 \mathtt{m^{3}}

We know that;

1 \mathtt{m^{3}} = 1000 liter

0.027 \mathtt{m^{3}} = 0.027 x 1000 = 27 liters

**Hence the volume of above cube is 27 liters**

**(02) Find the volume of below cuboid**

Given:

Length = 60 cm

Width = 30 cm

Height = 0.4 meter

Here length & width are given in centimeter, but height is given in meter.

**The units are inconsistent.**

Convert the height into centimeter

we know that;

1 meter = 100 cm

0.4 meter = 0.4 x 100 = 40 cm

**Now the dimension of cuboid is:**

Length = 60 cm

Width = 30 cm

Height = 40 cm

**Volume = Length x Breadth x Height**

Volume = 60 x 30 x 40 = 72000 \mathtt{cm^{3}}

**Hence 72000 \mathtt{cm^{3}} is the area of given cuboid**