Question

How many smaller cubes have less than three surfaces painted ?

• A. $8$
• B. $24$
• C. $28$
• D. $48$

Answer 1

Answer: (D)

$48$

Let the side of big cube be $4cm$. So, one side of smaller cube $=1cm$
$n=\frac{sideofbigcube}{sideofsmallcube}=\frac{4}{1}=4$.
Number of smaller cube having less than three surfaces painted = Number of smaller cubes having $2$ surfaces painted + Number of smaller cubes having one surface painted = Number of smaller cubes at $12$ edges + Number of smaller cubes at six surface.
$(n-2)\times 12+(n-2{)}^2\times 6$
$=24+24=48$.