Question

What is the side of a cube whose volume is 46656 cm square.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{s}=\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{cube} \\ \mathrm{Now}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{cube}=46656{\mathrm{cm}}^3 \\ \Rightarrow {\mathrm{s}}^3=46656 \\ \Rightarrow \mathrm{s}=\sqrt[3]{46656} \\ \Rightarrow \mathrm{s}=\sqrt[3]{\underline{2\times 2\times 2}\times \underline{2\times 2\times 2}\times \underline{3\times 3\times 3}\times \underline{3\times 3\times 3}} \\ \Rightarrow \mathrm{s}=2\times 2\times 3\times 3=36 \\ \mathrm{So},\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{cube},\mathrm{s}=36\mathrm{cm} \end{gathered}$$