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

## We have to find the height of the cylinder.Given:the radius of the sphere ($R$) $=4.2cm$the radius of cylinder ($r$) $=6cm$Solutionlet the height of the cylinder be $h$As given that the sphere is melted and recast into the shape of a cylinder.So,Volume of cylinder $=$ Volume of sphere$\pi {r}^{2}h=\frac{4}{3}\pi {R}^{3}\phantom{\rule{0ex}{0ex}}\pi {\left(6\right)}^{2}h=\frac{4}{3}\pi {\left(4.2\right)}^{3}36h=\frac{4}{3}\left(4.2×4.2×4.2\right)\phantom{\rule{0ex}{0ex}}h=1.4×1.4×1.4cm\phantom{\rule{0ex}{0ex}}h=2.74cm$Hence, the height of the cylinder is $2.74cm$.

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