Question

How many cubes have atleast two faces coloured ?

• A. $19$
• B. $20$
• C. $21$
• D. $23$

Answer 1

The correct option is C $21$

Let the side of the bigger cube be $5cm$. So, one side of smaller cube is $1cm$.
$\therefore n=\frac{sideofbigcube}{sideofsmallcube}=\frac{5}{1}=5$
Number of smaller cubes having atleast $2$ faces coloured = Number of smaller cubes having $3$ faces coloured + Number of smaller cubes having $2$ faces coloured = Number of smaller cubes at $6$ corners + Number of smaller cubes at $5$ edges.
$=6+(n-2)\times 5=6+3\times 5=6+15=21$