Question

A cone of height 24 cm and radius ob base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.​

Answer 1

☯ Let the radius of sphere be r cm.

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We know,

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• ${\sf{\bf{Volume\:of\:cone\:=\:{\dfrac{1}{3}}{\pi r}^{2}h}}}$

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$\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{\bigg (\:{\dfrac{1}{3}}\pi \:\times\:{6}^{2}\:\times\:24\:\bigg )}\sf\:{cm}^{3}$

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$\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{288\pi\:cm}^{3}$

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Then,

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• ${\sf{\bf{\red{Volume\:of\:Sphere\:=\:{\dfrac{4}{3}}{\pi r}^{3}\:{cm}^{3}}}}}$

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☆ Since the volume of the clay in the form of cone and the sphere is the same, therefore,

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$\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{\dfrac{4}{3}}{\pi r}^{3}\:=\:288\:\pi$

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$\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{r}^{3}\:=\:{6}^{3}$

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$\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{r\:=\:6}$

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$\:\therefore\:{\underline{\sf{Hence,\:the\:radius\:of\:the\:sphere\:is\:{\textsf{\textbf{6\:cm}}}}}}.$

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Answer 2

☯ Let the radius of sphere be r cm.

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We know,

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• ${\sf{\bf{Volume\:of\:cone\:=\:{\dfrac{1}{3}}{\pi r}^{2}h}}}$

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$\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{\bigg (\:{\dfrac{1}{3}}\pi \:\times\:{6}^{2}\:\times\:24\:\bigg )}\sf\:{cm}^{3}$

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$\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{288\pi\:cm}^{3}$

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Then,

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• ${\sf{\bf{\blue{Volume\:of\:Sphere\:=\:{\dfrac{4}{3}}{\pi r}^{3}\:{cm}^{3}}}}}$

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☆ Since the volume of the clay in the form of cone and the sphere is the same, therefore,

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$\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{\dfrac{4}{3}}{\pi r}^{3}\:=\:288\:\pi$

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$\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{r}^{3}\:=\:{6}^{3}$

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$\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{r\:=\:6}$

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$\:\therefore\:{\underline{\sf{Hence,\:the\:radius\:of\:the\:sphere\:is\:{\textsf{\textbf{6\:cm}}}}}}.$

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