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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.
cbse
class12
modelpaper
2008-1
sec-c
q24
math
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asked
Dec 29, 2012
by
thanvigandhi_1
edited
Jul 15, 2013
by
sreemathi.v
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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 height of the cylinder of maximum volume that can be inscribed in a cone of height \( h \: is \: \frac{1}{3}h\)
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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 \( \large\frac{4}{27}\pi h^3\tan^2 \alpha \).
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Feb 4, 2013
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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}$$ \pi \: h^3\: tan^2\: \alpha $
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Show that volume of the greatest cylinder which can inscribed in a cone of height h and semi-vertical angle $ 30^{\circ} \: is \: \large\frac{4}{81} $$\: \pi h^3.$
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Show that the rectangle of maximum area that can be inscribed in a circle is a square
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Prove that the height of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius R is \( \large\frac{2R}{\sqrt 3}.\) Also find the maximum volume.
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