Question

How many cubes will have atleast red colour on its surfaces ?

• A. $20$
• B. $22$
• C. $28$
• D. $32$

Answer 1

Answer: (C)

$28$

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 atleast red colour on its surfaces = Number of smaller cubes at $6$ corners + Number of smaller cubes at $2$ surfaces + Number of smaller cubes at seven edges.
$=6+(n-2{)}^2\times 2+(n-2)\times 7=6+8+14=28$.