Final answer:
The correct formula for the volume of a box with a square base and closed top is option A, which is V = l²h, as it is dimensionally consistent and accounts for the area of the square base and the height.
Step-by-step explanation:
The question concerns the determination of dimensional consistency of various formulas used to calculate volume and area, particularly in geometry. For the specific case of a box with a square base and closed top, the formula for the volume should account for the area of the square base (length squared) and the height. The correct formula would involve both these dimensions, hence option A, V = l²h, is dimensionally consistent. Option B, V = lwh, would apply to a rectangular box with differing lengths for length, width, and height. Option C, V = 2lwh, is dimensionally excessive, as there is no need for the coefficient 2 in a volume calculation. Lastly, option D, V = (l + w)h, does not make sense for a box with a square base, as the length and width are equal and therefore shouldn't be added together before multiplying by the height..