My understanding of the problem is that you want to use the surface you created as the top surface of your solid. I would have started my model a little differently but with what you have here is how I would achieve what you are looking for.
Here is a link to video of me doing it.
These commands are not on the standard feature ribbon by default and you can add them if you use them a lot, or do like I did and just use the command finder search bar.
Move the cutting surface to where you want it.
Use the surface to cut the solid into multiple bodies.
You can choose to consume the bodies you don't want during the cutting procedure or delete them later if needed.