Question

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.

Answer 1

Answer:

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