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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 is one-third that of the cone and the greatest volume of cylinder is `4/(27)pih^3tan^2alphadot`

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The correct Answer is:
`(4)/(27)pih^(3)tan^(2)theta.`
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MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-Misellaneous Exercise on Chapter (6)
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  9. Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 h...

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  10. Find the absolute maximum and minimum values of the function f give...

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  11. Show that the altitude of the right circular cone of maximum volume...

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  12. Let f be a function defined on [a, b] such that f^(prime)(x)>0, for al...

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  14. Show that height of the cylinder of greatest volume which can be insc...

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  15. A cylindrical tank of radius 10 m is being filled with wheat at the r...

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  17. The line y = m x + 1is a tangent to the curve y^2=4xif the value of m...

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  18. The normal at the point (1,1) on the curve 2y+x^2=3is(A) x + y = 0 (B)...

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  19. The normal to the curve x^(2)=4y passing (1, 2) is :

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  20. The points on the curve 9y^2=x^3, where the normal to the curve makes ...

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