Question

A cube A has side thrice as long as that of cube B. What is the ratio of the volume of cube A to that of cube B?

Answer 1

$$\begin{gathered} \mathrm{Suppose}\mathrm{that}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{side}\mathrm{of}\mathrm{cube}\mathrm{B}\mathrm{is}l\mathrm{cm}. \\ \mathrm{Then},\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{side}\mathrm{of}\mathrm{cube}\mathrm{A}\mathrm{is}3\times l\mathrm{cm}. \\ \mathrm{Now},\mathrm{ratio}=\frac{\mathrm{volume}\mathrm{of}\mathrm{cube}\mathrm{A}}{\mathrm{volume}\mathrm{of}\mathrm{cube}\mathrm{B}}\mathrm{=}\frac{(3\times l{)}^3{\mathrm{cm}}^3}{(l{)}^3{\mathrm{cm}}^3}\mathrm{=}\frac{{\mathrm{3}}^3\times l^3}{l^3}\mathrm{=}\frac{27}{1} \\ \therefore \mathrm{The}\mathrm{ratio}\mathrm{of}\mathrm{the}\mathrm{volume}\mathrm{of}\mathrm{cube}\mathrm{A}\mathrm{to}\mathrm{the}\mathrm{volume}\mathrm{of}\mathrm{cube}\mathrm{B}\mathrm{is}27:1. \end{gathered}$$