Question

a cone of height 24cm and radius base 6cm is made up of modeling clay a child reshapes it in the form of sphere. find radius of sphere

Answer 1

Volume of come=volume of sphere
1/3*22/7*6*6*24=4/3*22/7*r^3
6*6*6=r^3
r=6

Answer 2

Given: Radius & Height of cone is 6 cm and 24 cm respectively.

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》Let's consider the radius of sphere be R cm.

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$\begin{gathered}\underline{\boldsymbol{\bigstar\:According\:to\:the\:Question}}\\\\\end{gathered}$

A cone is reshaped in the form of sphere.

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Therefore,

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$\begin{gathered}:\implies\sf Volume\:of\:cone = Volume\:of\:cylinder\\ \\ \\ :\implies\sf \dfrac{1}{3} \times \cancel{\dfrac{22}{7}} \times (6)^2 \times 24 = \dfrac{4}{3} \times \cancel{\dfrac{22}{7}} \times R^3\\ \\ \\ :\implies\sf \dfrac{1}{\cancel{3}} \times 36 \times \cancel{24} = \dfrac{4}{3} \times R^3\\ \\ \\ :\implies\sf 36 \times 8 = \dfrac{4}{3} \times R^3\\ \\ \\ :\implies\sf R^3 = 36 \times \cancel{8} \times \dfrac{3}{\cancel{4}}\\ \\ \\:\implies\sf R^3 = 36 \times 2 \times 3\\ \\ \\:\implies\sf R^3 = 216\\ \\ \\:\implies\sf \sqrt[3]{R^3} = \sqrt[3]{216} \\ \\ \\:\implies{\underline{\boxed{\frak{\purple{R = 6\:cm}}}}}\\\\\\ \therefore\:{\underline{\sf{Radius\:of\:sphere\:formed\:is\: {\textsf{\textbf{6\:cm}}}.}}}\end{gathered}$

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$\begin{gathered}\qquad\qquad\qquad\boxed{\underline{\underline{\bf{\pink{\bigstar \: Formulas\:used\:\bigstar}}}}} \\\\\end{gathered}$

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

$\sf Volume\:of\:sphere = \bf{\dfrac{4}{3} \pi r^3}$