Cubes
Direction: 125 cubes of similar size are arranged in the form of the bigger cube (5 cubes on each side, i.e., 5 x 5 x 5) All the small cubes lying on the edge of the top layer of the bigger cube are removed and also cubes lying at the four corners of the bottom face are removed. All exposed faces of the block thus left are coloured red.
- How many small cubes are left in the block?
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Number of cubes removed from top face = 16
Number of cubes removed from bottom face = 4
Number of cubes left = 125 - (16 + 4 ) = 105Correct Option: D
Number of cubes removed from top face = 16
Number of cubes removed from bottom face = 4
Number of cubes left = 125 - (16 + 4 ) = 105
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.
- How many cubes are painted with yellow and blue?
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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
Out of 27 small cubes from 3 x 3 x 3, outer 26 cubes are 1st painted with blue and then it is kept back with original cube and painted with yellow so out of 26 cubes only 5 edges will give us cubes with both the colours and number of such cubes are 12Correct Option: C
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
Out of 27 small cubes from 3 x 3 x 3, outer 26 cubes are 1st painted with blue and then it is kept back with original cube and painted with yellow so out of 26 cubes only 5 edges will give us cubes with both the colours and number of such cubes are 12
- How many cubes are painted two faces only one with yellow and one with blue?
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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
Out of 12 cubes in previous question there are 4 cubes with 2 faces yellow so number of cubes painted two faces only one with yellow and one with blue is 12 - 4 = 8Correct Option: D
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
Out of 12 cubes in previous question there are 4 cubes with 2 faces yellow so number of cubes painted two faces only one with yellow and one with blue is 12 - 4 = 8
- What is the number of small cube with no face painted
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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 = 40Correct 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
Direction: 125 cubes of similar size are arranged in the form of the bigger cube (5 cubes on each side, i.e., 5 x 5 x 5) All the small cubes lying on the edge of the top layer of the bigger cube are removed and also cubes lying at the four corners of the bottom face are removed. All exposed faces of the block thus left are coloured red.
- How many cubes are with one face painted?
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From top face (out of 3 x 3 square face) only one cubes is with one face painted.
From 4 vertical faces each face will give us 6 cubes hence total number of cubes from vertical faces is 6 x 4 = 24.
From bottom face we will get 3 x 3 = 9 cubes
So total number of cubes with one face painted is 1 + 24 + 9 = 34Correct Option: A
From top face (out of 3 x 3 square face) only one cubes is with one face painted.
From 4 vertical faces each face will give us 6 cubes hence total number of cubes from vertical faces is 6 x 4 = 24.
From bottom face we will get 3 x 3 = 9 cubes
So total number of cubes with one face painted is 1 + 24 + 9 = 34
