1 cubic meter has actually 1000 liters that liquid. Meter is a unit live independence of kilogram.

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Then why does 1 liter of water in ~ max thickness (4 °C) have actually a fixed of 1 kg? Is that a just coincidence?

It is no a coincidence. Together the Wikipedia short article on the Litre says:

One litre that water has a mass of nearly exactly one kilogram when measured at its maximal density, which occurs at around 4 °C. Similarly: one millilitre (1 mL) that water has a fixed of about 1 g; 1,000 litres the water has a fixed of around 1,000 kg (1 tonne). This connection holds because the gram to be originally defined as the mass of 1 mL the water; however, this meaning was abandoned in 1799 due to the fact that the thickness of water transforms with temperature and, very slightly, with pressure.

1 liter that water equals $1 mathrmkg$ weight.1 liter of water is also the exact same as $1000 mathrmcm^3$ i.e. Cubic centimeter ($10 mathrmcm imes10 mathrmcm imes10 mathrmcm$ in volume) and1 liter is the same as 1 cubic decimeter (10 centimeters is 1 decimeter).

Therefore 1 cubic meter volume is the very same as 1000 cubic decimeter or 1000 liters and that is why 1000 liters that water weighs $1000 mathrmkg$ or 1 ton.Similarly, $1 mathrmcm^3$ is the exact same as $1 mathrmml$ and weighs $1 mathrm g$ the water.

It is not a just coincidence however a basic equivalence measurement in between the Metric system and the SI device of measurements.

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