i need to make the following conical hole using a cnc lathe.
the wider diameter should be approx 5/16" and the tip diameter (inside the 2.4" hole) shlould be approx 11/64" .
the material is brass.
what tools can i use to meke this hole?

Hi:
You could drill (undersize)to correct depth first, and then make a very small boring bar out of HSS.

regards

Maybe find a tapered pin or Morse taper reamer that would work for you. A Bridge & Boiler reamer is another possibility.

Edit:
Book on making reamers if you care to go that route.
http://books.google.com/books?id=ZE0OAAAAYAAJ&pg=PA59

If you do try a boring bar carbide would be better then HSS at that depth ratio, you have the advantage in that the bar could be tapered. Use shorter bars for most of the job.