question_answer 1)

Show that the right circular cone of least curved surface and given volume has an altitude equal to times the radius of the base.  

Answer:

Let r, h, l be the radius, height and slant height of the cone respectively.       Volume of cone (V) =  (Given)           ?.. (1)       Curved surface area of the cone (A) =                                                      (by (1))                          Let Z = A2 =                                     Now             Curved surface area (Z) of the cone is minimum when  Hence curved surface area of the cone will be minimum if  hence the result.