Final answer:
The statement about the least volume when a roller sits completely off the base is false. In geometry, an object's volume is determined by its dimensions, not its position relative to other objects.
Step-by-step explanation:
The question 'For the least volume, the roller sits completely off the base' appears to be related to a mathematical optimization problem, particularly concerning geometry and volume calculation. To determine the least volume configuration for an object like a roller, we need to examine how its position relative to a base affects its volume. The statement implies that there is a relationship between the position of the roller and the base that affects volume. However, in mathematical terms, the volume of a solid object like a roller is a fixed value, determined by its dimensions, and is not affected by its position relative to other objects. Therefore, the statement as given is False.