How many small cubes, each of 96 cm surface area, can be formed from the material obtained by melting a larger cube of 384 cm surface area ?

Answer: Option B

Let the length of each edge of small cube be a₁ and that of larger cube be a₂
Then,
$$\begin{array}{rl}& 6a_1^2=96\\ & \Rightarrow a_1^2=16\\ & \Rightarrow a_1=4and\\ & 6a_2^2=384\\ & \Rightarrow a_2^2=64\\ & \Rightarrow a_2=8\end{array}$$
∴ Number of cubes formed :
$$\begin{array}{rl}& =\frac{\text{Volume of larger cube}}{\text{Volume of smaller cube}}\\ & =\left(\frac{8\times 8\times 8}{4\times 4\times 4}\right)\\ & =8\end{array}$$