The SI unit of measure for volume is the 'Litre'.
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You use for example cm3. So yeah, use the little three at the end since the shape has three dimensions.
A ruler or meter stick can be used to measure a rectangular prism. Just measure and plug into L*W*H=Volume
You would typically use liters or gallons to measure the volume of a hot tub.
The basic unit of volume is the cubic metre. In everyday use, the litre is more common.
You would use liters (L) to measure the volume of a soda container in the metric system.
You don't use a unit of mass to measure a volume. Mass and volume are two different things. Mass is measured in kilograms. The main unit of volume in the SI is the cubic meter, but for a kettle, the liter (= cubic decimeter, or 1/1000 of a cubic meter) can be used instead.
There is no unit of measure, and no mechanical device, that can describe or measure both mass and volume.