Question

The dimensions of a metallic cuboid are $100\mathrm{cm}\times 80\mathrm{cm}\times 64\mathrm{cm}$. It is melted and recast into a cube. Find the surface area of the cube.
[CBSE 2011]

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{edge}\mathrm{of}\mathrm{cube}\mathrm{be}a. \\ \mathrm{As}, \\ \mathrm{Volume}\mathrm{of}\mathrm{cube}=\mathrm{Volume}\mathrm{of}\mathrm{cuboid} \\ \Rightarrow a^3=100\times 80\times 64 \\ \Rightarrow a^3=512000 \\ \Rightarrow a=\sqrt[3]{512000} \\ \Rightarrow a=80\mathrm{cm} \\ \mathrm{Now},\mathrm{the}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cube}=6a^2 \\ =6\times 80\times 80 \\ =38400{\mathrm{cm}}^2 \end{gathered}$$

So, the surface area of the cube is 38400 cm².