Q15 of 168 Page 242

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is .

Let R and h be the radius and the height of the cone respectively.


The volume (V) of the cone is given by;


V =


Now, from the right triangle BCD, we get,


BC =



V =






Now, if , then,









Now,


Now, when , it can be shown that < 0.


Therefore, the volume is the maximum when .


When,


Height of the cone = r + .


Therefore, it can be seen that the altitude of the circular cone of maximum volume that can be inscribed in a sphere of radius r is.


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