Question

Explain the relation between $litre,d{m}^3$ and $ml.$

Answer 1

Step 1: Find the relation between $\mathit{l}\mathit{i}\mathit{t}\mathit{r}\mathit{e}$ and $\mathit{d}{\mathit{m}}^{\mathbf{3}}$:

• Both $m^3$and $litre$are units of volume and $1m^3=1000litres$.
• $1d{m}^3={\left(1\times {10}^{-1}m\right)}^3$ ( $\because$‘d’ stands for deci i.e. ${10}^{-1}$ )

$$\begin{gathered} ={10}^{-3}{m}^3 \\ ={10}^{-3}\times {10}^{3}litres \end{gathered}$$

$\Rightarrow 1d{m}^3=1litre$ …[1]

Step 2: Find the relation between $\mathit{l}\mathit{i}\mathit{t}\mathit{r}\mathit{e}$ and $\mathit{m}\mathit{l}$ :

• $1ml={10}^{-3}litre$ ($\because$ ‘m’ stands for milli i.e. ${10}^{-3}$ )

$=\frac{1}{1000}litre$

$\Rightarrow 1litre=1000ml$ …[2]

• From [1] and [2], we can say that, $1litre=1d{m}^3=1000ml.$

Hence, $\mathbf{1}\mathbf{}\mathit{l}\mathit{i}\mathit{t}\mathit{r}\mathit{e}\mathbf{=}\mathbf{1}\mathbf{}\mathit{d}{\mathit{m}}^{\mathbf{3}}\mathbf{=}\mathbf{1000}\mathbf{}\mathit{m}\mathit{l}\mathbf{.}$