A cone of height $20\ cm$ and radius of base $5\ cm$ is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.


 Radius of the cone $=r=5\ cm$


Height of the cone $=h=20\ cm$

Let the radius of the sphere $=R$

As per given statement,

Volume of sphere $=$ volume of cone
 
$\Rightarrow \frac{4}{3}\pi R^{3}=\frac{1}{3}\pi r^{2}h$

$\Rightarrow 4R^{3}=5^{2}\times20$

$\Rightarrow 4R^{3}=500$

$\Rightarrow R^{3}=\frac{500}{4}$

$\Rightarrow R^{3}=125$

$\Rightarrow R=\sqrt[3]{125}$

$\Rightarrow R = 5\ cm$

$\therefore$ Diameter of the sphere $=2R=2\times5=10\ cm$

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Updated on: 10-Oct-2022

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