Question

How many spheres 12 cm in diameter can be made from a metallic cylinder of diameter 8 cm
and height 90 cm​

Answer 1

Answer:

720cm...................

Answer 2

$\tt\small{It\: is \:given\: that, }$

$\tt\small{\bold{Diameter\: of\: the \:sphere \:=\: 12cm}}$

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• $\tt\small{\bold{Radius\: of\: the \:sphere}}$ $\tt\small{=}$ $\tt\frac{12}{2}\:=\:6\:cm$

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$\tt\small{We\: know \:that :}$

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• $\tt\small{\bold{Volume\: of\: the \:sphere}}$ $\tt\small{=}$$\tt\frac{4}{3}π$${r}^{3}$

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$\tt\small{By \:substituting \:the\: values ,}$

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• $\tt\small{\bold{Volume\: of\: the \:sphere}}$ $\tt\small{=}$$\tt\frac{4}{3}×$$\frac{22}{7}×$$\tt{6}^{3}$

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$\tt\small{So\: we \:get,}$

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• $\tt\small{\bold{Volume \:of\: the \:sphere}}$$\tt\small{= \:905.142}$$\tt{cm}^{3}$

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$\tt\small{It \:is \:given\: that:}$

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• $\tt\small{\bold{Diameter\: of\: the \:cylinder}}$$\tt\small{= \: 8cm}$

• $\tt\small{\bold{Radius\: of\: the \:cylinder }}$$\tt\small{=}$ $\tt\frac{8}{2}$$\tt\small{= \:4cm}$

• $\tt\small{\bold{Height \:of\: the \:cylinder }}$$\tt\small{= \:90cm}$

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$\tt\small{We\: know \:that,}$

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• $\tt\small{\bold{Volume \:of\: the \:cylinder }}$$\tt\small{=}$$\tt{πr}^{2}$h

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$\tt\small{By\: substituting \:the\: values: }$

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• $\tt\small{\bold{Volume\: of\: the \:cylinder }}$$\tt\small{=}$ $\tt\frac{22}{7}\:×$ $\tt{4}^{2}$$\tt\small{× \:90}$

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$\tt\small{So\: we\: get ,}$

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• $\tt\small{\bold{Volume \:of\: the \:cylinder}}$$\tt\small{= 4525.714 }$$\tt{cm}^{3}$

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$\tt\small{We\: know \:that ,}$

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• $\tt\small{\bold{Number\: of \:spheres }}$$\tt\small{=}$ $\tt\small\frac{Volume\: of \:cylinder}{ Volume \:of\: sphere}$

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$\tt\small{By \:substituting \:the\: values:}$

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• $\tt\small{\bold{Number\: of \:spheres }}$$\tt\small{=}$ $\tt\frac{4525.714}{905.142}$$\tt\small{= \:5}$

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$\tt\small\pink{Therefore, \:5\: spheres \:can\: be \:made\: from }$$\tt\small\pink{a\: metallic\: cylinder.}$