Let R and h be the radius and the height of the cone respectively.
The volume (V) of the cone is given by;
Now, from the right triangle BCD, we get,
Now, if , then,
Now, when , it can be shown that < 0.
Therefore, the volume is the maximum 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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