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.
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To find the dimensions of a box that contains twice as many cubes as a 2x3x4 box, we first calculate the volume of the smaller box: 2 x 3 x 4 = 24 cubic units. Since the larger box contains twice as many cubes, its volume must be 2 x 24 = 48 cubic units. To determine the dimensions of the larger box, we need to find three numbers that multiply together to give 48. One possible set of dimensions could be 4 x 4 x 3, as 4 x 4 x 3 = 48 cubic units.
A side (2-dimensions) or edge (3-dimensions).
The 2x4's I use measure 1 and a half by 3 and a half.
area is 2, volume is 3
11 3/4 top x 10 3/8 bottom x 14 1/2 deep in