Volume is measured in what units?

What is Volume?

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

what is volume in Math

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

define units of volume

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}}

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

what is the unit of volume

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.

what is liter

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}}


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

Relation between cubic meter and liter

Example Explanation
Consider the below aquarium whose water is filled to the brim.
Find the volume of water filled in liters

explain liter in math

Observe that the aquarium is in the form of cuboid

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

relation between liter and milliliter

Units of Volume – Questions

(01) Find the volume of below cube in liters

Volume of cube question math

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

Math question on volume of cuboid

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

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