What is the Area formed when a line is traced between two 3D curves?

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Volume/Area between two hyperbolic paraboloids

This question is quite related to intersection of cylinders, Hyperbolic paraboloid and modelling.

I am welding a trunnion to a pipe (both are hollow cylinders in different geometry). They intersect along their axis at 90 deg (no offset).

The trunnion has a groove at 45 deg as shown in fig extending from the ID to OD. So when the trunnion seat on the pipe, the ID of the trunnion forms a saddle curve. When the 45 deg groove extends to the OD from the ID, it also forms a saddle curve on the OD of the Trunnion.

Now how to find the volume contained inside the solid trunnion? I think i have explained myself clear. Kindly put your queries or solution.

Simeon welded trunnion