If I understand correctly, in order to get the volume of your remaining area you should first compute the resulting mesh. This is known as boolean operations which are often implemented on envelopes (surface mesh like in the .obj files)
There is several python modules proposing implementations for boolean operation on meshes.
- pymesh exposes the algorithms of CGAL (c++ library)
- pymadcad with a different algorithm in pure python
- blender which is a complete software but which provide boolean operations in their API
- trimesh relying on CGAL and Blender
there is few other modules but - as far as I know - all of them are relying on pymesh or blender under the coat.