Hi,

I'm confused on how to calculate the center of mass of a solid that's located out of one sphere and into another. The problem goes on like this:

Determine the center of mass of a solid located out of a sphere, of radius 1, centered at the origin, and inside a sphere, of radius 1, centered at point $\displaystyle \left(0,0,1\right)$.

All I get from my textbook is the mass formula:

$\displaystyle m=\int\int\int_{E} \rho(x,y,z)\mathrm{d}V$

And then if the center of mass is actually the same thing as a center of inertia, I would have to calculate the moments related to each plan of coordinates.

How can I do that when I've got two spheres one above the other. I believe their equations are respectively:

$\displaystyle x^2+y^2+z^2=1$

and

$\displaystyle x^2+y^2+(z-1)^2=1$

As plotted below.

Can you please give me a hint? I'm blocked there.

Thanks a lot,

Bazinga