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A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted ?

A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted ? Correct Answer 8

Let the each side of original cube be 12 units.

According to the question, the cube is cut into 36 cubes such that 32 cubes are small and 4 cubes are big.

Each of 32 small cubes will have sides of 3 units.

Each of 4 big cubes will have sides of 6 units each. None of the faces of big cube is painted blue.

This arrangement can be shown with the help of following diagram :

 

[ alt="F1 Sonali.S 19-02-21 Savita D1" src="//storage.googleapis.com/tb-img/production/21/02/F1_Sonali.S_19-02-21_Savita_D1.png" style="width: 347px; height: 284px;">

Therefore, the number of cubes having only one face painted is 8.

Hence, 8 is the correct answer.

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