The inertia for a point mass is [tex]I = mr^{2}[/tex]. If you have a sphere you can treat it as a large number of point masses and add them together as in [tex]I = \sum m_{i}r_{i}^{2}[/tex]. It is probably better to solve this using calculus though. For rotational inertia the equation [tex]I = \sum m_{i}r_{i}^{2}[/tex] is an approximation of [tex] I = \int r^{2} dm [/tex].
Rotational inertia is also related to kinetic energy. Kinetic energy can be expresses as [tex]K = \frac{1}{2} I \omega^{2}[/tex] where [tex]\omega[/tex] is the angular speed.
I've never heard anyone say that there 18 ways to solve this problem, but I suppose it might depend on what other information you might be given.
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