# A cube is coloured on one face Orange, Pink on opposite face

A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. now, answer the following questions based on the above statements:

How many cubes have at least one face coloured pink ?

nikhil4nigam Profile Answers by nikhil4nigam Questions by nikhil4nigam

• Member Since Feb-2010 | Mar 5th, 2010

Since we are going to divide the cube into 125 small equal cubes.
we have to cut the cube in a particular format.

125=5*5*5

Hence we have to cut it 5 equal cuts in lengthwise then 5 equal cuts in breadthwise and 5 equal in thickness wise.

Now since only one face is pink colored .So by this manner analysing we are getting 25 cubes will have at least one face pink colored.

Concept behind this particular problem is that  just calculate wheather the no. of smaller cubes given is a cube of any no. or not. If YES then answer will be square of that no and if the given smaller no. of cubes is square of any no. then answer will be that  square.

#### nikhil4nigam Profile Answers by nikhil4nigam

• Mar 5th, 2010

Since we are going to divide the cube into 125 small equal cubes.
we have to cut the cube in a particular format.

125=5*5*5

Hence we have to cut it 5 equal cuts in lengthwise then 5 equal cuts in breadthwise and 5 equal in thickness wise.

Now since only one face is pink colored .So by this manner analysing we are getting 25 cubes will have at least one face pink colored.

Concept behind this particular problem is that  just calculate wheather the no. of smaller cubes given is a cube of any no. or not. If YES then answer will be square of that no and if the given smaller no. of cubes is square of any no. then answer will be that  square.  