A cube is painted with green colour on it's five faces. If this cube is cut into equal 125 small cubes. How many small cubes will have no face coloured.

27 faces have no face colored

Step-by-step explanation:

Divide the cube into 125 parts. This can be done by dividing the length, breadth and height of the cube in 5 equal parts each.

A cube painted green on all faces, is divided into 125 small cubes. l x bx h = 125

L = 5, B = 5, H = 5

A cube has 6 faces

Let A & B be 1st pair of opposite lateral faces

C & D be 2nd pair of opposite lateral faces

E be Top face

F be bottom face

Now we find out the total number of colored faces =

Face A contains = 25 cubes (l x h = 5x5)

Face B contains = 25 cubes (l x h = 5x5)

Face C contains = 15 cubes (b x h = 3 x5)

Face D contains = 15 cubes (b xh = 3x5)

Face E contains = 9 cubes (l x b = 3x3)

Face F contains = 9 cubes (l x b = 3x3)

So total number of painted faces = 25+25+15+15+9+9 = 98 cubes

The number of cubes not painted on any of the faces = 125 - 98 = 27