Check this out: http://www.toledometalspinning.com/hopper/default.php
The cone should be 60 degrees (read that somewhere).
It is steep enough to allow yeast and trub to slide and settle towards the apex of the cone (though you sometimes see pro-brewers whacking the larger cones with rubber mallets to try and get the yeast and trub to settle further down the cone).
Keep in mind that, given the same radius and height, the volume of a cylinder is 3 times that of a cone.
You can ferment more beer in less space with a cylinder.
This is an important consideration if you're using a keezer or refrigerator.
To use a 27 gallon fermentor, you'd need 24 x 24 x 36 inches (minimum), preferably 26x26x38 inches or more. See the Blichman website listed below (click on "data" tab).
If doing it from scratch, I'd basically copy the profile of a 20 gallon brew kettle and put a 60 degree cone on the base; basically giving yourself a 26.67 gallon fermentor (assuming you go with a flat lid).
Consider using FermCap-S to limit the excessive krausen -- it'll help prevent blow-off problems.
Check out the 27 gallon fermentor Blichmann makes http://www.blichmannengineering.com/fermentor/fermentor.html