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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 `alpha` is one - third that of the cone and the greatest volume of cylinder is `(4pi)/(27)h^(3) tan^(2)alpha`.

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The correct Answer is:
`= (4)/(27)pi h^(3)tan^(2)alpha`
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KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -MISCELANEOUS EXERCISE - 6
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