Project a flat surface on a conical surface

I would ask for your collaboration to find out how to project a flat surface onto a conical surface.
The surface its not the same at the base and top

you could try the drape tool (part of the sandbox tools) or push pull the shape into the pole and intersect the two pieces and delete any excess.

The screen shows a tube with a base as one component. Rectangle tool, Push/pull 1/32"; Circle tool, Push/pull 5"; Erase internal face between tube and base; Done.