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

A sphere of fixed radius (*r)* is given.

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 have:

∴*h*

∴ The volume is the maximum when

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

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