Can't say for sure about the 3" bend radius, (if I were buying hose off
the shelf I'd just give it bend and see how it behaved), but there is a
chance that a 3" radius translates into a 6" diameter. (This may be a
wrong assumption, and some engineer will wade in to clarify).

To me, the radius of a curve describes the severity of the arc measured
from a central point in the turn, not the hose on the other side of the
turn. But I may be wrong- the only thing I studied in geometry class
was the backside of the gal who wound up doing my homework. :-)