I'd like to calculate the radii or the difference of the radii (thickness of spherical shell) of 2 concentric spheres where the only given value is the volume between the concentric spheres (spherical shell). The inner sphere has a constant volume (non-zero).
I know the volume of the spherical shell's equation would be like this:
$V = 4/3\pi(R^3-r^3)$
I thought this formula might be involved for the cubic differences of the radii
$(x^3-y^3) = (x-y)(x^2+xy+y^2)$
Which would lead to this:
$V = 4/3\pi(R-r)(R^2+Rr+r^2)$
I'm not sure where to go from here. I would also be happy to know if there are any alternative methods for the solution.