Question

If the total surface area of a cube is 54x2 then find its lateral surface area.

Answer 1

$$\begin{gathered} \mathrm{Let}s=\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{each}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{cube} \\ \mathrm{now},\mathrm{total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cube}=6s^2 \\ \mathrm{but}\mathrm{total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{cube}=54x^2 \\ \Rightarrow 6s^2=54x^2 \\ \Rightarrow s^2=9x^2 \\ \Rightarrow s=3x \\ \mathrm{now},\mathrm{lateral}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cube}=4s^2=4{\left(3x\right)}^2=4\times 9x^2=36x^2 \end{gathered}$$