A solid is bounded on the top by the paraboloid $z=r^{2},$ on the bottom by the plane $z=0,$ and on the sides by the cylinder $r=1 .$ Find the center of mass and the moment of inertia about the $z$ -axis if the density is a. $\delta(r, \theta, z)=z$

b. $\delta(r, \theta, z)=r$