What are the Spherical Coordinates for a Quarter Ball Volume?

[mrkb80]

Homework Statement

I am having so much trouble with this one problem ( and spherical coordinates in general ).

Any help would be amazing:
∫∫∫ 1 / √(x²+y²+z²)

Over -4≤x≤4, 0≤y≤√(16-x²), 0≤z≤√(16-x²-y²)

Homework Equations

The Attempt at a Solution

I know that rho² will replace √(x²+y²+z²) in my integral, but I am having a really hard time understanding what my limits of integration should be for rho,phi, and theta. I think it is some sort of a snow cone, where theta is from 0 to pi/2 but I'm really not sure.

 

[mrkb80]

I found a very similar problem which helped me solve: http://www2.seminolestate.edu/lvosbury/CalculusIII_Folder/CylindricalSpherical.htm

 

[Quinzio]

Your volume is a quarter of a ball. A ball cut in 4 pieces by two ortogonal planes.
This is 0<rho<4, 0<theta<pi, 0<phi<pi/2