a cube of 6 cm is painted of all its 6 faces with red colour . it is then broken up into 216 smaller identical cubes .what is the number of smaller cubes with no coloured surface ,number of smaller cubes with 1 red face and number cubes with 2 red faces .

Answer 1

We have a cube of 6 cm broken into 216 cubes (of 1cm cubed), meaning each face is divided into 6x6=36 small squares.
The interior cube that has no paint therefore has a size of 4 cm cubed, or 64 cubic cm.
The cubes that have paint on two sides would be the middle four along each of the 12 edges (i.e. excluding the corners).
The cubes which have paint on one side would be the middle cubes of each face (16 cubes per face) There are six faces.

All these should add up to 208 cubes. Together with the 8 corners (with 3 faces painted), there will be 216 cubes.