Integration Coupling Variables

I am trying to find the volume of a spherical shell using Comsol 4.3a in a 2D axisymmetric coordinate system. I attempted to do this by creating a integration coupling variable along the boundary of the shell with the expression pi*r^2, but it returns a value that is significantly different from the expected 4/3*pi*r^3. Can anybody help me find the volume contained within the boundary of a spherical shell?

Incidentally, integrating along the boundary with the expression 2*pi*r for the surface area returns the expected value, as does integrating the contained subdomain with the expression 2*pi*r for the volume, but I would like to be able to calculate the volume using boundary integration.

Thanks in advance,
Sean MacGahan