a conical drinking cup is made from a circular piece of paper of
radius 3 inches by cutting out a sector and joining the edges of the
removed sector. find max volume

Interesting homework problem. Here is one way to proceed. Figure out
how the height of the cone depends on the radius of the base. Computer
the volume. Figure out which radius gives the maximum volume.
Obviously both 0 and 3 inches have zero volume, but values in between
do not.

when they give the radius of 3 inches. that isnt the radius of the
cone right? its the radius of the circular paper.  right ? so wouldnt
that be the height

nevermind.  i cut myself a diagram out of paper  :)