Spherical Coordinates and Centre of Mass

[JaysFan31]

Wondering if someone could help me get this answer. I don't get spherical coordinates at all.

The volume of the region given in spherical coordinates by the inequalities
3 less than or equal to rho less than or equal to 5
0 less than or equal to phi less than or equal to pi/6
-pi/6 less than or equal to theta less than or equal to pi/6
is filled with uniform material. Find the x-coordinate of the centre of mass.

Thanks for any help.

John

 

[siddharth]

You need to show your work before you get help. What are your thoughts/ideas on this problem?

 

[JaysFan31]

Ok. I know that the centre of mass is the triple integration of density x-bar over just the triple integration of the mass. I guess I don't know what the density function is. I'm pretty sure that x=rhosin(phi)cos(theta).

I'll integrate with the given bounds. But what is the density function?

 

[NateTG]

Well, what happens if the density is 1 (with appropriate units)?

 

[HallsofIvy]

You will also need to know that the "differential of volume" in spherical coordinates is
$$\rho^2 sin(\phi)d\rho d\theta d\phi$$
(I'm sure that's in your textbook!)