Just deleted my former answer and its edits because it asked and quessed, but did not gave results.Here is a better one:
Illustrator can't give wanted result as 3D rendering, because this is an intersection of 2 volumes. Illustrator produces only one at a time and no combinations are possible in illustrator.
If the final volume could be produced equivalently as only one revolution or extrusion but maybe starting accordingly from more complex shape, then it would be possible to get perfect rendering from illustrator, too. But this is not the case. Those 2 volumes are sub 90 degrees revolutions, but around different axels. That makes the right pre-revolving combination nonexistent.
If another or both volumes were thin, like the last piece of a cake, then an approximate volume could be rendered in Illustrator. Thislike:
Generally correct result can only be got from 3D CAD software. The paid Sketchup is more than good enough, but also some high quality freebies exist. Note: Free Skethcup can't add, subtract or intersect 3D voulumes except only in some trivial cases.
A high quality 3D freebie is Design Spark Mechanical. The global electronic component dealer has put out their own heavily stripped version of SpaceClaim, which is a top notch non-parametric 3D direct modeller. Design Spark's version is still VERY powerful, altough a well thought set of features are disbled to prevent serious large scale pro applications. Some missing features:
- motion kinetics
- automatic 2D drawings
- realistic photographic rendering
- materials for rendering and mass calculations
- sheet metal
- export & import as editable SpaceClaim compatible file
Much is off, but EUR 0,00 instead of EUR 2500,- creates deep pardon absolution and forgiveness.
The following solution of questioner's volume intersection popped out in 2 minutes; so easy is the interface if for example Sketchup is familiar.
viewing angle is selected for seeing 3 surfaces.
To complete the Illustrator version. I tried to add coordinate axels and one xy plane circle as a bed for the volume. It was so annoying that I gave up. In 3D it's possible to insert these and much more needed detail easily. When they are ready, the finale in Illustrator is an easy overdraw job.