Answer
(a) greater
(b) III
Work Step by Step
(a) We know that the moment of inertia is greater when the mass is farther from the axis. Thus, the moment of inertia about the rim of the wheel is greater than the moment of inertia about the axle.
(b) We know that the best explanation is option (III) -- that is, the mass is farther from the axis when the wheel is rotated about the rim.