A cube is coloured red on one face, green on the opposite face, yellow on another face and blue on a face adjacent to the yellow face. The other two faces are left uncloured. It is then cut into 125 smaller cubes of equal size.

  1. How many cubes are uncoloured on all the faces?
  2. How many cubes have at least two colored faces?
  3. How may cubes are clolured red on one face ad have the remanng faces uncoloured?
  4. How mayny cubes ave least one green face?
  5. How many cubes are clolured blue on one face, red or green on another face and have four uncoloured faces.

Can youplease answer my questions with explanations. (any 3)

Here the cube is divided into 125 parts, so if you consider a big cube, then cut four equal marks vertically and four marks horizontally. You will get a cube of 125 parts.

1) Uncoloured cubes
the cube is uncoloured from two sides , and the inside cubes are also uncoloured, so you will get 48 cubes like this,which are uncoloured.

2)How many cubes are coloured blue on one face, red or green on another face and have four uncoloured faces.
These are the cubes which are edges cube, Blue on one face is compulsion and can have either red or green on other face.
You will get 8 cubes like this.

You can do others similarly.

 

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