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 cubes with exactly one face painted?
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- 36
- 66
- 42
- 45
Correct Option: B
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
In original big cube number of faces with one colour is 3(6 -2)2 = 48 (here we have considered only 3 untouched of big cube)
But here we have removed a cubes of the form of 3 x 3 x 3 and again put it back so out of three new exposed faces of big cube we will have 4 cubes in each face that is painted with one colour hence number of cubes from these three surfaces is 3 x 4 = 12
Now consider out of 3 x 3 x 3 cubes we will have 6 cubes (one in each face ) which are painted only one face.
Hence total number of cubes = 48 + 12 + 6 = 66
