question_answer 89)

Show that semi-vertical angle of the cone of given surface area and maximum volume is sin?1.

Answer:

Let be the semi-vertical angle of cone with radius r, height h, slant height l.         Given: Surface area of cone                           Volume of cone = V =                                      (Using (1))                         Let                   2Ar =       A =                                   (by (1))                                           Now              is maximum when       Hence semi-vertical angle of cone of maximum volume is  hence the result.