Question

A cone and a hemisphere have equal bases and equal volumes . Find the ratio of their length .​

Answer 1

Answer:

Surface Areas and Volumes

Let the radius of both cone and hemisphere be r cm. Let h be the height of the cone. Hence, the ratio of the heights of a cone and hemisphere is 2 : 1.

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• Cone and hemisphere has equal bases and equal volumes .

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

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• Ratio of length = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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$\sf{\red{\boxed{\bold{Volume\: of \: cone = \dfrac{1}{3}\pi r^2h}}}}$

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$\sf{\red{\boxed{\bold{Volume\: of \: cone = \dfrac{2}{3}\pi r^3}}}}$

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$\sf : \implies\: {\bold{ \dfrac{1}{3} \pi r^2h = \dfrac{2}{3}\pi r^3}}$

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$\sf : \implies\: {\bold{ \dfrac{1}{3} r^2h = \dfrac{2}{3}r^3}}$

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$\sf : \implies\: {\bold{ r^2h = 2r^3}}$

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$\sf : \implies\: {\bold{ h = \dfrac{ 2r^3}{r^2}}}$

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$\sf : \implies\: {\bold{ h = 2r}}$

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length of the cone = height = 2r

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length of the hemisphere = radius = r

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Ratio of length of cone : length of hemisphere

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2r : r

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2 : 1

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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• Ratio of the lengths = 2 : 1