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A solid cube has been painted yellow, blue and black on pairs of opposite faces. The cube is then cut into 36 smaller cubes such that 32 cubes are of the same size while 4 others are of the bigger size. Also, no face of any of the bigger cubes is painted blue.
Q. How many cubes have at least one face painted blue?
- a)0
- b)8
- c)16
- d)32
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A solid cube has been painted yellow, blue and black on pairs of oppos...
The figure is divided into three layers. The First layer in the front consisting of 16 cubes has:
(i) 4 central cubes having one face painted blue and all other faces uncoloured.
(ii) 4 corner cubes having one face blue, one face yellow, one face black and the remaining three faces uncloured
(iii) Out of the remaining cubes, 4 cubes have one face yellow and one face blue and all other faces
uncloured while 4 cubes have one face black and one face blue and all other faces uncoloured.
The second layer in the middle consisting of 4 cubes each of which has one face black and one
face yellow and all other faces uncoloured.
The third layer in the lear consisting of 16 cubes has exactly the same configuration as the first layer.
All the 16 cubes in the first layer and all the 16 cubes in the third layer have at least one face painted blue.
Thus, there are 16 + 16 = 32 such cubes
(i) 4 central cubes having one face painted blue and all other faces uncoloured.
(ii) 4 corner cubes having one face blue, one face yellow, one face black and the remaining three faces uncloured
(iii) Out of the remaining cubes, 4 cubes have one face yellow and one face blue and all other faces
uncloured while 4 cubes have one face black and one face blue and all other faces uncoloured.
The second layer in the middle consisting of 4 cubes each of which has one face black and one
face yellow and all other faces uncoloured.
The third layer in the lear consisting of 16 cubes has exactly the same configuration as the first layer.
All the 16 cubes in the first layer and all the 16 cubes in the third layer have at least one face painted blue.
Thus, there are 16 + 16 = 32 such cubes
Most Upvoted Answer
A solid cube has been painted yellow, blue and black on pairs of oppos...
The figure is divided into three layers. The First layer in the front consisting of 16 cubes has:
(i) 4 central cubes having one face painted blue and all other faces uncoloured.
(ii) 4 corner cubes having one face blue, one face yellow, one face black and the remaining three faces uncloured
(iii) Out of the remaining cubes, 4 cubes have one face yellow and one face blue and all other faces
uncloured while 4 cubes have one face black and one face blue and all other faces uncoloured.
The second layer in the middle consisting of 4 cubes each of which has one face black and one
face yellow and all other faces uncoloured.
The third layer in the lear consisting of 16 cubes has exactly the same configuration as the first layer.
All the 16 cubes in the first layer and all the 16 cubes in the third layer have at least one face painted blue.
Thus, there are 16 + 16 = 32 such cubes
(i) 4 central cubes having one face painted blue and all other faces uncoloured.
(ii) 4 corner cubes having one face blue, one face yellow, one face black and the remaining three faces uncloured
(iii) Out of the remaining cubes, 4 cubes have one face yellow and one face blue and all other faces
uncloured while 4 cubes have one face black and one face blue and all other faces uncoloured.
The second layer in the middle consisting of 4 cubes each of which has one face black and one
face yellow and all other faces uncoloured.
The third layer in the lear consisting of 16 cubes has exactly the same configuration as the first layer.
All the 16 cubes in the first layer and all the 16 cubes in the third layer have at least one face painted blue.
Thus, there are 16 + 16 = 32 such cubes
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Community Answer
A solid cube has been painted yellow, blue and black on pairs of oppos...
The figure is divided into three layers. The First layer in the front consisting of 16 cubes has:
(i) 4 central cubes having one face painted blue and all other faces uncoloured.
(ii) 4 corner cubes having one face blue, one face yellow, one face black and the remaining three faces uncloured
(iii) Out of the remaining cubes, 4 cubes have one face yellow and one face blue and all other faces
uncloured while 4 cubes have one face black and one face blue and all other faces uncoloured.
The second layer in the middle consisting of 4 cubes each of which has one face black and one
face yellow and all other faces uncoloured.
The third layer in the lear consisting of 16 cubes has exactly the same configuration as the first layer.
All the 16 cubes in the first layer and all the 16 cubes in the third layer have at least one face painted blue.
Thus, there are 16 + 16 = 32 such cubes
(i) 4 central cubes having one face painted blue and all other faces uncoloured.
(ii) 4 corner cubes having one face blue, one face yellow, one face black and the remaining three faces uncloured
(iii) Out of the remaining cubes, 4 cubes have one face yellow and one face blue and all other faces
uncloured while 4 cubes have one face black and one face blue and all other faces uncoloured.
The second layer in the middle consisting of 4 cubes each of which has one face black and one
face yellow and all other faces uncoloured.
The third layer in the lear consisting of 16 cubes has exactly the same configuration as the first layer.
All the 16 cubes in the first layer and all the 16 cubes in the third layer have at least one face painted blue.
Thus, there are 16 + 16 = 32 such cubes
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A solid cube has been painted yellow, blue and black on pairs of opposite faces. The cube is then cut into 36 smaller cubes such that 32 cubes are of the same size while 4 others are of the bigger size. Also, no face of any of the bigger cubes is painted blue.Q.How many cubes have at least one face painted blue?a)0b)8c)16d)32Correct answer is option 'D'. Can you explain this answer?
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Solutions for A solid cube has been painted yellow, blue and black on pairs of opposite faces. The cube is then cut into 36 smaller cubes such that 32 cubes are of the same size while 4 others are of the bigger size. Also, no face of any of the bigger cubes is painted blue.Q.How many cubes have at least one face painted blue?a)0b)8c)16d)32Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Railways.
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