Answer
36.86 kilograms
Work Step by Step
a) We find the minimum mass, which would be if it had the shape of a wheel:
$I=mr^2 \\ m = \frac{I}{r^2}=\frac{7.8}{.46^2} =\fbox{36.86 kilograms}$.
b) The moment of inertia is maximized when the mass is a long ways from the axis of rotation, so it could have more mass if more of the mass was closer to the axis of rotation.
