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Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.

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Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.

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Let radius of sphere = r

height of cone = x

radius of base of cone = y

Diameter of sphere and axis of cone will coincide with each other that by maximum height can be taken.

= 2 : 3 or height of cone is 2/3 of diameter of the sphere.

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