Can I use Guldinus Theorem to calculate the z co-ordinate of the center of mass of a homogeneous solid,
for example, if I have $D = \{(x, y, z) \in \mathbb{R}^3 : 1 ≤ x^2 + y^2 + z^2 ≤ 9, z ≥ 0 \}$,
how can I proceed to calculate the z coordinate of the centre of mass ? I have used this formula
$Za = \int \frac{zdxdydz}{V(a)}$
and I went to polar co-ordinates , can someone help me to do all the calculation so I see if I understood the concept ?