Question

State any two smaller units of volume. How are they being related to the S.I units?

Answer 1

Hint: we can obtain smaller units for volume by considering the length of the sides to be in centimetre or millimetre or decimetre. Therefore the volume will be in the units of centimetre or in decimetre or any of the smaller units we provide for the length of the sides. And also their relationship should be found by conversion method.

Complete step by step answer:
 A smaller unit of volume can be given in cubic centimetre and cubic decimetre.
$1c{{m}^{3}}=1cm\times 1cm\times 1cm$
The relationship between ${{m}^{3}}$ and $c{{m}^{3}}$ can be written as,
As we know,
$1{{m}^{3}}=1m\times 1m\times 1m$
Let us convert metre into centimetre now,
$1{{m}^{3}}=100cm\times 100cm\times 100cm$
Calculating this will give the relation between ${{m}^{3}}$ and $c{{m}^{3}}$,
$1{{m}^{3}}={{10}^{6}}c{{m}^{3}}$
Therefore one unit has been calculated,
Now let us look at another unit in which the decimetre is there as the length of the side of the cube.
As we all know,
$1m=10dm$
And also the metre cube can be written as,
$1{{m}^{3}}=1m\times 1m\times 1m$
Now let us covert this metre into decimetre,
$1{{m}^{3}}=10dm\times 10dm\times 10dm$
After making simplification and calculating this will give,
$1{{m}^{3}}={{10}^{3}}d{{m}^{3}}$
Therefore the two units have been calculated. They are $1d{{m}^{3}}$ and $1c{{m}^{3}}$. Also their relationship has also been found out.

Note: A cubic centimetre is a generally used unit of volume that is not the SI units which can be corresponding to the volume of a cube that is calculated as $1cm\times 1cm\times 1cm$. One cubic centimetre is equal to a volume of one millilitre. The mass of one cubic centimetre of water is closely equivalent to one gram at a temperature of $3.98{}^\circ C$. One cubic centimetre is the volume of a cube which is having a side $1cm$. The description of a decimetre is one tenth of a meter in length.