Question

A cube of side $5cm$ is painted on all its faces. If it is sliced into $1cubiccentimetre$ cubes, how many $1cubiccentimetre$ cubes will have exactly one of the side painted.

• A. $27$
• B. $42$
• C. $54$
• D. $142$

Answer 1

The correct option is C

$54$

The cube side = $5cm$

The volume of cube $=5^3=125c{m}^3$

When it is sliced into $1cubiccm$, then

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{smaller}\mathrm{cubes}=\frac{\mathrm{Volume}\mathrm{of}\mathrm{bigger}\mathrm{cube}}{\mathrm{Volume}\mathrm{of}\mathrm{smaller}\mathrm{cube}} \\ \mathrm{Number}\mathrm{of}\mathrm{smaller}\mathrm{cubes}=\frac{125}{1}=125\mathrm{cubes} \end{gathered}$$

In one face of cube, there are total of $9$ small cubes painted.

We know that, there are $6$ faces in cube.

Thus, total of $9\times 6=54$ faces will have one face painted.

Thus, option C is correct.