Name: Melis

Who is asking: Student
Level: Middle

I'm confused about questions like these:

1. 2by2by2 cube:

If this cube was painted blue on the outside,

  • how many cubes would have 3 blue faces
  • 2 blue faces
  • 1 blue face
  • 0 blue faces
I do not understand how to do this question!!!!! Please help me!

Hi Melis

  The simplest way to solve this problem is to build the cube using 8 blocks (e.g. 8 dice or 8 sugar cubes) and then paint the outside of the cube, or at least imagine what would happen if you painted the outside of the cube. If you don't have blocks you could find a box that is in the shape of a cube and draw the edges of the blocks on each of the 6 faces of the cube. This would mean that each face would have 4 congruent squares drawn on it. Perhaps just a sketch would do. If you think of the 8 blocks that form the cube you will realize that none of them is completely hidden. So if you spray-painted the outside of the big cube then every small cube would have some paint on it. So no small cubes would have 0 faces painted. You can figure out the rest of the problem.
  Once you understand what is happening here, build a 3by3by3 cube using 27 blocks and paint the outside. How many of the 27 blocks have no paint on them? How many have 3 sides painted blue? ...

Jack and Penny

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