Cubic metres are used to measure the volume of a fluid, or kilograms for the mass. This is true for the volume and mass of a gas, liquid or solid.
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The liter is NOT a true SI unit of measure. See : http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf for more information.
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A liter is a measure of volume, so the simple (and annoying) answer is one liter. It is also equal to 1000 ml. If you took a cube 10 cm on a side and filled it with water, you'd have one liter of water. In US measurements, it is about 1.06 liquid quarts.
The volume of liquids can be measured in liters or cubic centimeters, cubic decimeters, or cubic meters. 1 liter = 1 cubic decimeter.
I would say that liters are used for measuring how much space an object takes (volume), like milliliters.
Volume and capacity are essentially the same. So you could say the litre is a suitable unit for both.
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