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Question
A cube of side 4 cm is painted on all its sides. If it is sliced in 1 cubic cm cubes, then number of such cubes that will have exactly two of their faces painted is ______.
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Solution
A cube of side 4 cm is painted on all its sides. If it is sliced in 1 cubic cm cubes, then number of such cubes that will have exactly two of their faces painted is 24.
Explanation:
The volume of a cube of side 4 cm = 4 × 4 × 4 = 64 cm3 When it is sliced into 1 cm3 cubes, we will get 64 small cubes.
In each side of the larger cube, the smaller cubes in the edges will have more than one face painted.
The cubes which are situated at the corners of the big cube, have three faces painted.
So, to each edge two small cubes are left which have two faces painted. As, the total number of edges in a cube are 12.
Hence, the number of small cubes with two faces painted = 12 × 2 = 24
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