An aluminium sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference in the surface areas of the two solids would be :

Answer: Option C

Volume of cube = Volume of sheet = (27 × 8 × 1) cm³ = 216 cm³
Edge of cube :
$$\text{root}3\text{of}216cm=6cm$$
Surface area of sheet :
$$\begin{array}{rl}& =2\left(lb+bh+lh\right)\\ & =2\left(27\times 8+8\times 1+27\times 1\right)\text{ c}{\text{m}}^2\\ & =\left(216+8+27\right)\text{ c}{\text{m}}^2\\ & =502\text{ c}{\text{m}}^2\end{array}$$
Surface area of cube :
$$\begin{array}{rl}& =6a^2\\ & =\left(6\times 6^2\right)\text{ c}{\text{m}}^2\\ & =216\text{ c}{\text{m}}^2\end{array}$$
∴ Required difference :
$$\begin{array}{rl}& =\left(502-216\right)\text{ c}{\text{m}}^2\\ & =286\text{ c}{\text{m}}^2\end{array}$$