Final answer:
The true or false statement about the roller's position lacks context, but typically, an object like a roller would not be stable if situated only halfway on its base and halfway behind it.
Step-by-step explanation:
The question seems to be addressing the position of a roller in relation to its base, which could be part of a mathematics problem involving geometry or physical objects. The statement, 'For medium volume, the roller sits halfway on its base and halfway behind the base' suggests a position that is equidistant from two reference points. However, the provided options (a, b, c, d) do not clearly relate to the true or false nature of the statement. Without additional context or a diagram, it is difficult to definitively answer whether the statement is true or false. Nonetheless, if we are to interpret 'halfway' as indicating the roller's center of mass being aligned with the edge of the base, then the statement could be interpreted as false, as one would expect the roller to either sit completely on its base or completely behind it for stability, not half-and-half.