Question

# the radius and height of a metallic cylinder are 4.2 cm and 5.6 cm respectively. it is melted and recast into a sphere. find the radius of the sphere

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Solution

## $\mathrm{After}\mathrm{recast},\phantom{\rule{0ex}{0ex}}\mathrm{Volume}\mathrm{of}\mathrm{cylinder}=\mathrm{volume}\mathrm{of}\mathrm{sphere}\phantom{\rule{0ex}{0ex}}{\mathrm{\pi r}}^{2}\mathrm{h}=\frac{4}{3}{\mathrm{\pi r}}^{3}\phantom{\rule{0ex}{0ex}}4.2×4.2×5.6=\frac{4}{3}×{\mathrm{r}}^{3}\phantom{\rule{0ex}{0ex}}{\mathrm{r}}^{3}=74.08\phantom{\rule{0ex}{0ex}}\mathrm{r}=4.19\mathrm{cm}$

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