Question

A wooden cube is painted with purple on all the four adjoining faces and yellow on two opposite faces

then it is into 216 identical smaller cubes then how many cubes are there having two different colour​

Answer 1

Answer:

6^3-4^3

=152

Step-by-step explanation:

216=6^3(total cube pieces)

4^3=64

(these were not visible before the cube was cut. So they have single wood colour)

so we have

216-64=152 cubes of 2 colours

and 6^2= 36

so we have each face of the original cube cut into 36 smaller cubes.

Each edge will be 1/6 of original length.

Now the colours:

(1)cubes cut from original yellow faces:

The peripheral 20 pieces cut from each yellow face will have purple and yellow(ie 2 colours)

so 40 pieces from 2 faces will have these colours.=.........=40

But the central 16 pieces from each yellow face will also have 2 colours each(yellow on outer original face and wood colour ie shade of brown on inner wood which is now cut, exposed and visible after cutting the original cube.

so 16x2x2=64..................=64