Question

if V denotes the volume of the cube & S its surface area. show that V= S/6* √s/6

Answer 1

$$\begin{gathered} \mathrm{Suppose}\mathrm{side}\mathrm{of}\mathrm{a}\mathrm{cube}=\mathrm{a}\mathrm{units} \\ \mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{a}\mathrm{cube}\left(\mathrm{S}\right)=6{\mathrm{a}}^2 \\ \mathrm{Volume}\mathrm{of}\mathrm{a}\mathrm{cube}\left(\mathrm{V}\right)={\mathrm{a}}^3\mathrm{cubic}\mathrm{units} \\ ={\mathrm{a}}^2\times \mathrm{a} \\ =\frac{\mathrm{S}}{6}\times \frac{\sqrt{\mathrm{s}}}{\sqrt{6}} \\ =\frac{\mathrm{S}\sqrt{\mathrm{S}}}{6\sqrt{6}} \end{gathered}$$