Then has boundary , which is orientable, but is not simple solid. However, we can write

where

Then and are both simple solids, is bounded by piecewise smooth surfaces upper hemisphere of the surface upper hemisphere of and the annulus surface in the -plane given by

Similarly, is bounded by , the lower hemisphere of , the surface , the lower hemisphere of and . Note that the outward normal on as boundary of is negative of the outward normal of as boundary of . The divergence theorem is applicable to both and , and we set