Question

If all the faces of a cube are painted, and 9 cuts are made on it such that the cube gets divided into
maximum number of identical cubes. How many small cubes will not have any painted faces?​

Answer 1

Answer:

Step-by-step explanation:

2 cube +3cube+ 4cube + 5cube =

2cube =8

3cube=27

4cube=64

5cube=125

8+27+64+125=324

Answer 2

Four small cubes will not have any painted faces.

If all the faces of a cube are painted, and 9 cuts are made on it such that the cube gets divided into maximum number of identical cubes.

We have to find the small cubes not have any painted faces.

There are three axes in 3d geometry. these are x , y and z - axis. If we make three cuts in parallel to each axis, we will get 9 cuts and 64 small cubes.

now the question said,“ all faces of bigger cube are painted. so the small cubes directly attached to faces of bigger cube will be coloured.

see the diagram, here you can observe, only four such types of smaller cubes which doesn't have any coloured face.

Therefore four small cubes will not have any painted faces.