A big cube painted with yellow colour in all sides. if you
cut it into 1000 cubes with same dimension. than how many
cubes were without painted anyside. explain it?
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Answer Posted / shreyas
there are 508 cubes which are not painted on any of the sides.
the cube has 6 sides.
If the cube is divided into 1000 cubes, then every side will show 100 sides of the small cubes.
Remember that the cubes on the edges share faces with more than one side of the big cube.
Every side of the big cube has 100 sides of the smaller cubes out of which 36 are on the edges and share sides with other sides of the big cube.
so remove all the cubes which are on the edges.
i.e. 1000-(36+26+26+10+10)= 892
now consider the inner faces that are painted, each side of the big cube is left with 64 sides of the small cubes.
so 892-(64*6)= 508
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