Question

The unit used to measure the liquids is litre. One litre is equal to 1000 millilitre and one millilitre is equal to 1 cm${}^3$. Deduce a relationship between S.I. unit of volume and litre.

• A. $1m^3=10L$
• B. $1m^3=10ml$
• C. $1m^3=1000L$
• D. $1c{m}^3=1L$

Answer 1

Answer: (C)

$1m^3=1000L$

Given, 1 litre $=$ 1000 ml .......... (1)
($ml=$ millilitre) and 1 m$l=$ 1 cm${}^3$ .......... (2)
Substitute (2) in (1) we get,
1 litre $=$ 1000 cm${}^3$ ........... (3)
We know that, S.I. unit of volume $=$ m${}^3$
Now, we have to find, 1 litre $=$ ? m${}^3$
We know,
1 m $=$ 100 cm
$\Rightarrow (1m{)}^3=(100cm{)}^3$
$\Rightarrow 1m^3=1000000c{m}^3$ ........... (4)
Dividing (3) by (4) we get,
$\frac{1litre}{1m^3}=\frac{1000c{m}^3}{1000000c{m}^3}$
$\frac{1000}{1000000}=\frac{1}{1000}$
$\Rightarrow \frac{1litre}{1m^3}=\frac{1}{1000}$
$\Rightarrow 1000litre=1m^3$ or
$1litre=\frac{1}{1000}{m}^3={10}^{-3}{m}^3$
$\therefore 1litre={10}^{-3}{m}^3$ or $1m^3={10}^{3}litre$