show that the cone of greatest volume which can be inscribed in a given sphere has an altitude =2/3RD of diameter of sphere.

Let be the centre of the sphere of radius* r*.

Also let ACB be the height of the cone

ACB = *h *units

BC = *h – r*

Let *s* be the radius of the cone

Now, volume of the cone,

In ABCD,

Putting value of *s*^{2} in equation (1)

For maximum volume,

where, *d* = diameter of the sphere

Hence, cone of greatest volume which can be inscribed in a given sphere has an altitude (diameter) of the sphere.

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