Although the prompt is false, it often takes students a long time to find a counter-example. Classes have decided to explore 'small' cuboids by drawing 2-d representations of the cuboids and their nets. The conclusion follows that the statement is true. However, it is not true for a cube of side length 6 units and thereafter.
This is another inquiry that teaches students to think about the structure of the mathematical object under inquiry. As one student has commented, "we need to visualise a case in which the space inside the cuboid is getting bigger while the surface area remains the smallest possible."
An important point to make in this inquiry (occasionally made by a student) is that we are comparing the numerical values of two different units of measure - an observation that can lead to a productive discussion in a key stage 3 class.
In the classroom, students have suggested extending the inquiry by considering other solids. Cylinders might be easier than triangular prisms to use because the latter require knowledge of Pythagoras' Theorem to calculate the surface area accurately.