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it doesn't have a volume since it is flat.

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"volume" only makes sense in a three-dimensional world.

'mm' is a one-dimensional measure of distance.

In a 3D world, the volume is expressed in [mm^3].

For example, a cube with 1 mm per edge will have the volume of 1 mm^3.

A line of 1 mm long will have a volume of exactly zero, in a 3D world.

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Q: What does one millimeter have a volume of?
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