I'm not sure how to solve this problem -
The paraboloid $$ z =r^2,\;r \le a$$ has constant density $\delta$. Find its centroid and moment of inertia around the $z$-axis.
I think that this has already been paramaterized with cylindrical co-ordinates, so I could try solving
$$ \iint r^2\delta dS $$
But it doesn't come out to the answer.
How should I do this problem?