Direction: 343 Small unpainted cubes are arranged to from a large cube. All the six faces of the large cube are painted white. Now, a 3 x 3 cube, comprising 27 small cubes, is removed out from one of the corners of the large cube. The 3 x 3 cubes is now painted blue on all six faces, while all the three surface (each of which a is a 3 x 3 square) of the large cube exposed due to the removal of the 3 x 3 cube are painted black. Then, the 3 x 3 cube is put back in its original position in the large cube and the large cube is finally painted yellow on all the six faces.
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What is the number of small cube with no face painted
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- 40
- 18
- 20
- 14
Correct Option: A
Initial total number of cubes = 343,
Number of cubes removed = 27
Smaller 27 cubes painted blue
Exposed faces of original big cube (3 faces with 9 cube on each face i.e total 27 cubes) painted with black
Without any changes number of cubes with no face colour is given by (6 - 2)3 = 64
Now because of removal of 3 x 3 x 3 cubes from one of the corner from each face that were not painted earlier got exposed and will get painted, so from 3 x 3 x 3 cubes 4 x 3 = 12 cubes got painted, and a similar number from 3 exposed faces of big cube got painted.
Total number of cubes with no face painted is 64 - 12 - 12 = 40
