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Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone

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Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle a is one-third that of the cone and α the greatest volume of cylinder is \(\frac{4}{27}\pi h^3\)

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Height of cone – h 

Radius of cone – r 

Height of cylinder – y 

Radius of cylinder – x

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