Question

Fill in the following - \[1{{m}^{3}}=\text{ }............\text{ liters}\]

Answer 1

Hint: Understand the significance of $ {{m}^{3}} $ and then know the relation between cubic meter and liter. One unit, meters is a measurement of length while the other, liters is measurement of volume. But when the unit meter is multiplied three times, it becomes equal to the unit of volume.

Complete step-by-step answer:
Question concerns with the unit conversion. Conversion of one unit to another. Before going to unit conversion, let us first understand some basic things.
Units like meter or m is a measurement of length, for example 6m length of scale.
But, if we multiply meter with meter itself it will become \[{{\left( \text{meter} \right)}^{2}}\Rightarrow {{m}^{2}}\]
 $ {{m}^{2}} $ is no longer a measurement of length, but here 2 lengths are being indicated. So, this will give us the measurement of an area, for example: a park with dimension $ 12m\times 13m $
Similarly, if we multiply another meter in $ {{m}^{2}} $ it would become $ {{m}^{3}} $ Now $ {{m}^{3}} $ indicates there are 3-dimensions given. A 3-dimensional network is nothing but volume. Example: a cuboid \[2m\times 3m\times 4m\Rightarrow {{m}^{3}}=\text{Volume}\]
Since, we know liters are measurements of volume. Therefore, we can relate these two units that are $ {{m}^{3}} $ and liters. And, it is predefined.
\[\Rightarrow 1{{m}^{3}}=1000\text{ liters}\]

Note: Cubic meter or $ {{m}^{3}} $ is a metric system volume unit.
\[1{{m}^{3}}=1000\text{ L}\]
Similarly, 1 liter can be converted into $ {{m}^{3}} $
\[\begin{align}
  & \Rightarrow 1{{m}^{3}}=1000\text{ liters} \\
 & \Rightarrow 1\text{ liter = 1}{{\text{0}}^{\text{-3}}}{{m}^{3}} \\
\end{align}\]