Question

How many cubes will have no side painted ?

• A. $18$
• B. $16$
• C. $22$
• D. $8$

Answer 1

The correct option is A $18$

Total number of smaller cubes
$=\frac{4\times 4\times 4}{1\times 1\times 1}=64$
$n=\frac{sideofbigcube}{sideofsmallcube}=\frac{4}{1}=4$.
Number of smaller cubes having no side painted = Number of smaller cubes from inside the cube + Number of smaller cubes at $2$ surfaces + Number of smaller cubes at one edge
$=(n-2{)}^3+(n-2{)}^2\times 2+(n-2)\times 1$
$=8+8+2=18$.