Question

A cube of edge 4cms is painted externally it is then cut into one cm cubes. How many of these do not have red paint on any face?
A.4 B.8 C.56. D.16
[Question from AMTI-2006]​

Answer 1

when we divide we get 4x4x4 little cubes, so it’s 64 cubes.

The corner cubes all of them have 3 faces painted, so that’s 8 cubes.

64–8=56

The middle cubes all have 1 side only painted, and we have 4 of these for each cube face, so thats 4x6= 24

56–24=32

We have to remove the inner cubes that have no ink at all, and thats 8 cubes

32–8=24

These 24 left, all of them have 2 sides with paint!