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The dimensions are the length width and height of the prism. So if the prism is halfed then you would have to cut the dimensions in half depending on where the prism was cut.
You can't tell the dimensions of a rectangle from its area, or the dimensions of a prism from its volume.
Like you would a regular prism.
If the ratio of the dimensions of the larger prism to the smaller prism is r then the ratio of their volumes is r^3.
Just knowing the volume in centimeters cubed of a rectangular prism would not allow you to find the dimensions.