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Show that the volume of the greatest cylinder that can be inscribed in a cone of height 'h' and semi-vertical angle \( \alpha \) is \( \large\frac{4}{27}\pi h^3\tan^2 \alpha \).
cbse
class12
modelpaper
2012
sec-c
q24
math
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asked
Feb 4, 2013
by
thanvigandhi_1
edited
Jul 29, 2013
by
sreemathi.v
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Show that the volume of the greatest cylinder which can be inscribed in a cone of height h and semivertical angle $ \alpha, \: is \: \large\frac{4}{27}$$ \pi \: h^3\: tan^2\: \alpha $
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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 $\large \frac{4}{27}$$\pi h^3 \: tan^2 \: \alpha $
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Show that the volume of greatest cylinder which can be inscribed in a cone of height h and semi vertical angle $\alpha\;is\;\frac{4}{27}\pi h^3\tan ^2\alpha$
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Show that the height of the cylinder of maximum volume that can be inscribed in a cone of height h is \( \large\frac{1}{3}h.\)
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Show that the volume of the greatest cylinder which can be inscribed in a cone of height h and semi vertical angle $ 30^\circ\;is\;\large\frac{4}{81}\pi h^3$
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