Question

How many smaller cubes have atleast one surface painted with green colour ?

• A. $8$
• B. $24$
• C. $32$
• D. $56$

Answer 1

The correct option is C $32$

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 cubes having at least one surface painted with green xolour = Number of smaller cubes at $8$ corners + Number of smaller cubes at $8$ edges + Number of smaller cubes at $2$ surfaces
$=8+(n-2)\times 8+(n-2{)}^2\times 2=8+16+8=32$