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# Write the relation between ‘liter’ and ‘$cm^3$’

Last updated date: 02nd Aug 2024
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Hint: A liter is equal to a cubic decimeter. Note that, we can easily convert centimeters into decimeters and convert it into liters.
On the other hand, a cubic centimeter is the same as a milliliter. Here we can convert milliliters into liters and find the relation between cubic centimeters and liters.

Complete step-by-step solution:
A liter is defined as a special name for a cubic decimetre or ($10$ centimeters $\times$ $10$ centimeters $\times$ $10$ centimeters) ($1{\text{ }}L \equiv 1{\text{ }}dm3 \equiv 1000{\text{ }}cm3$ ).
Hence $1{\text{ }}L{\text{ }} \equiv 0.001{\text{ }}m3{\text{ }} \equiv 1000{\text{ }}cm3$ ,
and $1m^3$ (i.e. a cubic meter is the SI unit for volume) is the same as$1000L$ .
To convert between $cm^3$ and liters, it is helpful to know that a $cm^3$ is the same as a milliliter$\left( {mL} \right)$.
$1cm^3 = 1mL$
and the relation between $mL$ and $liters$ is
$1000mL = 1{\text{ }}L$
Therefore the conversion factor between $cm^3{\text{ }}and{\text{ }}L$ is $1000cm^3{\text{ }} = 1{\text{ }}L$

Note: Liter is the derived unit of cubic meter cube and milliliter is the derived unit of cubic centimeter cube.