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If, by 'metric system', you mean the 'SI system', then there is no base unit for volume. The unit for volume is called a 'derived unit', and it is the cubic metre (m3).
What is the metric unit for liquid volume of a sink
The cubic meter is the only standard unit of volume in the SI.The liter is a non-SI unit, but it is officially acceptedand may be used with metric prefixes.
Liters are the metric unit for liquid volume or more strictly dm3. ------------------------------------------------------------------------------------------------- The litre (symbol L or l, the first is preferred) is not a true SI-unit; it is only an "accepted" unit of volume. 1 cubic metre (symbol m3, the SI unit) has 1 000 litres.
The basic unit of the liter is the liter itself. The liter is a unit of volume in the metric system, and is equal to one cubic decimeter.