36
Question
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 bigger sizes. Also no faces of any of the bigger cubes is painted blue.
How many cubes have no face painted ?
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 bigger sizes. Also no faces of any of the bigger cubes is painted blue.
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Solution
The correct option is D 0
In the given statement, there are 36 cubes, 32 of which are of the same size and 4 other sure of bigger size. Clearly, each side of bigger cubes is twice as large as that of similar cubes. Also, since no face of any of the larger cubes is painted blue, so each one of the larger cubes has one face painted red, one is black and all other faces are unpainted.
The number of cubes having atleast one of the faces painted are 16 cubes, each along the surfaces painted blue 4 larger cubes. Thus there are (16×2)+4=36 cubes having atleast one of the faces painted. Since, there are 36 cubes in all, therefore, number of cubes having no face painted =36−36=0.
In the given statement, there are 36 cubes, 32 of which are of the same size and 4 other sure of bigger size. Clearly, each side of bigger cubes is twice as large as that of similar cubes. Also, since no face of any of the larger cubes is painted blue, so each one of the larger cubes has one face painted red, one is black and all other faces are unpainted.
The number of cubes having atleast one of the faces painted are 16 cubes, each along the surfaces painted blue 4 larger cubes.
Thus there are (16×2)+4=36 cubes having atleast one of the faces painted.
Since, there are 36 cubes in all, therefore, number of cubes having no face painted =36−36=0.
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