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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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