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