33.  A conical drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB.  Find the maximum capacity of such a cup.

h^2 + r^2 = R^2                                        V(h) = (Pi)(r^2)(h)/3
           r^2 = R^2 - h^2                                       = (Pi)(R^2 - h^2)(h) / 3
                                                                            = (Pi)(R^2h - h^3) / 3
                                                                  V'(h) = (Pi)(R^2 - 3h^2)/3

Critical numbers:
        (Pi)(R^2 - 3h^2)/3 = 0
                    R^2 - 3h^2 = 0
                             -3h^2 = -R^2
                                h^2 = (R^2)/3
                                    h = sqrt[(R^2)/3]
                                    h = R/ sqrt(3)

V[R/ sqrt(3)] = (Pi)(R^2h - h^3) / 3
                       = (Pi)[(R^2)(R/ sqrt(3)) - (R/ sqrt(3))^3] / 3
                       = (Pi)[(R^3)/ sqrt(3) - (R^3) / 3 sqrt(3)] / 3
                       = (Pi)([(3R^3) - (R^3)] / 3 sqrt(3)) / 3
                       = (Pi)(2R^3/ 3 sqrt(3)) / 3
                       = 2Pi R^3 / 9 sqrt(3)                          maximum volume in terms of R