$3)(35$ pts$\backslash ()\backslash )$ The $\backslash (25-\backslash$mathrm$\{$kg$\}\backslash )$ thin$-$walled ring below has a radius of $0\mathrm{.}75$ m $.$ At the bottom edge, a $\backslash (0\mathrm{.}2-\backslash$mathrm$\{$m$\}\backslash )$ diameter sphere with a mass of $4$ kg has been welded on$.$ Determine the mass moment of inertia about the z$-$axis:

a$.$ Passing through the center of mass of the section.

b$.$ Passing through the center of the ring $($Point C$).$

c$.$ Passing through the center of the sphere $($Point A$)$

d$.$ Comparing your answers to b and c $,$ is it easier to rotate the shape about the center of mass of the ring or the sphere? Why is this the case?