Final answer:
The correct formula for volume that matches the dimensionality of length³ is V = IWH, where V represents volume, and I, W, and H represent lengths.
Step-by-step explanation:
The student is trying to remember the formula for the volume of a three-dimensional object, which is usually expressed in terms of lengths of sides and heights. When considering the options given (V = IWH, V = I²WH, V = IWH², V = I(WH)), it's clear that the dimensionally consistent formula for volume must result in a value with three dimensions of length, that is, length × width × height (l × w × h). Therefore, the correct formula is V = IWH, which matches the dimensionality of volume (length³).
The other options, V = I²WH and V = IWH², suggest additional squares of length, leading to incorrect dimensional analysis since volume is not represented by length to the fourth or fifth power. The option V = I(WH) is dimensionally consistent as well, but often the parentheses are used for clarification and do not change the actual operation since multiplication is associative