Question

A cube of white material is painted red on all its surfaces. If it is cut into 125 smaller cubes of same size, then how many cubes will have two sides painted red?

Accepted Answer

D. $n = \sqrt[3]{125} = 5$. Cubes with exactly 2 faces painted lie on the edges (excluding corners). Number of such cubes = $12(n - 2) = 12(5 - 2) = 36$.

Painted Cube Cutting

Explanation

Practise this under exam conditions