Question

A cube of side $4cm$ is painted on all its sides. If it is sliced in $1cubiccm$ cubes, then number of such cubes that will have exactly two of their faces painted is __________.

Answer 1

The cube side = $4cm$

The volume of cube $=4^3=64c{m}^3$

When it is sliced into $1cubiccm$, then

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{smaller}\mathrm{cubes}=\frac{\mathrm{Volume}\mathrm{of}\mathrm{bigger}\mathrm{cube}}{\mathrm{Volume}\mathrm{of}\mathrm{smaller}\mathrm{cube}} \\ \mathrm{Number}\mathrm{of}\mathrm{smaller}\mathrm{cubes}=\frac{64}{1}=64\mathrm{cubes} \end{gathered}$$

Now, you can see that,

On each side of the larger cube, the smaller cubes in the edges should have more than one face painted.

Therefore, the cube which is located at the corner of the larger cube has three faces painted.

Hence, on each edge, two small cubes are left, in which two faces are painted.

It is known that the total number of edges in cubes $=12$

Thus, the number of small cubes with two faces painted $=12\times 2=24$ small cubes.