A cone of radius 3 cm and height 7 cm is melted and recast into a cube. Find the side of the cube.

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Please find below the solution to the asked query:
$$\begin{gathered} \mathrm{Volume} \mathrm{of} \mathrm{cone}=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=\frac{1}{3}\times \frac{22}{7}\times {\left(3\right)}^2\times 7=66 {\mathrm{cm}}^3 \\ \mathrm{Now} \mathrm{cone} \mathrm{is} \mathrm{melted} \mathrm{and} \mathrm{recast} \mathrm{into} \mathrm{cube} \mathrm{so} \mathrm{volume} \mathrm{of} \mathrm{cone}=\mathrm{volume} \mathrm{of} \mathrm{cube} \\ \mathrm{Volume} \mathrm{of} \mathrm{cube}={\left(\mathrm{side}\right)}^3 \\ \mathrm{Hence} \\ \Rightarrow {\left(\mathrm{side}\right)}^3=66 \\ \Rightarrow \mathrm{Side}=\sqrt[3]{66}=4.04 \mathrm{cm} \left(\mathrm{Answer}\right) \end{gathered}$$

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