Length, width and depth.
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The are no dimensions: the result is a pure number which is 24. "2 by 3 by 4" is a numerical expression: there are no dimensions associated with any of the three numbers and so there are no dimensions in their products.
area is 2, volume is 3
Volume has three dimensions - width, height and depth.
3
A side (2-dimensions) or edge (3-dimensions).