A spherical shell whose inner radius is 2 cm and whose outer radius is 8 cm is made of material of varying density.

At a point {x, y, z}, the density of the material is 0.39 times the square of the distance to the center of the sphere.

Assume all the air has been pumped out of the hollow interior.

Does the shell sink or float in water?

This is an integration that's meant to be done in spherical coordinates.