Question

A wooden cube with edge length ‘n’ (>2) units is painted red all over. By cutting parallel to faces, the cube is cut into $n^3$ smaller cubes each of unit edge length. If the number of smaller cubes with just one face painted Red is equal to the number of smaller cubes completely un painted, then n=

• A. 2
• B. 7
• C. 8
• D. 6

Answer 1

The correct option is C

8

Number of cubes obtained from one face which are painted on only one side = $(n-2{)}^2$
No. of cubes which are unpainted = $(n-2{)}^3$
$(n-2{)}^2\times 6=(n-2{)}^3$
$\Rightarrow n-2=6\Rightarrow n=8$