Question

A metallic sphere of radius $4.2cm$ is melted and recast into the shape of a cylinder of radius $6cm$. Find the height of the cylinder.

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Solution

Given:Radius of sphere $=4.2cm$Radius of cylinder $=6cm$Also given that the object formed by recasting the sphere will be the same in volume.So, Volume of Sphere $=$ Volume of Cylinder.$\left(\frac{4}{3}\right)\pi {r}^{3}=\pi {r}^{2}h\phantom{\rule{0ex}{0ex}}\left(\frac{4}{3}\right)\pi {\left(4.2\right)}^{3}=\pi {\left(6\right)}^{2}h\phantom{\rule{0ex}{0ex}}h=\frac{4×{\left(4.2\right)}^{3}}{3×12}={\left(1.4\right)}^{3}$h $={\left(1.4\right)}^{3}=2.744cm$Hence, the height of the cylinder is $2.744cm$.

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