Question

A cube of side $5cm$ is painted on all its faces. If it is sliced into $1$ cubic centimetre cubes, then how many $1$ cubic centimetre cubes will have exactly one of their faces painted?

(a) $27$

(b) $42$

(c) $54$

(d) $142$

Answer 1

Given, a cube of side $5cm$ is painted on all its faces and is sliced into $1c{m}^3$ cubes and cubes will have exactly one of their faces painted.

i.e., Little cubes with exactly one painted side.

So, we need to leave the corner squares of each face.

So, there exist $9$ cubes from each face.

observe the following figure.

Since, there are six faces available.
Hence, total number of smaller cubes $=6\times 9=54$

Hence, option C is correct.