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Question
A 10cm×10cm×10cm wooden block is painted red on all of its faces. It is then cut into cubes, 1cm on each edge.
How many cubic centimetre pieces have exactly 2 faces painted?
A 10cm×10cm×10cm wooden block is painted red on all of its faces. It is then cut into cubes, 1cm on each edge.
How many cubic centimetre pieces have exactly 2 faces painted?
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Solution
The correct option is A 96
From the figure it is clear that to each edge of the big cube 10 small
cubes are connected and two out of them are situated at the corners of
the big cube which have all three faces painted.
Thus, to edge two small cubes are left which have two faces painted. As the total no. of edges in a cube are 48.
Hence the no. of small cubes with two faces coloured =48×2=96
From the figure it is clear that to each edge of the big cube 10 small
cubes are connected and two out of them are situated at the corners of
the big cube which have all three faces painted.
Thus, to edge two small cubes are left which have two faces painted. As the total no. of edges in a cube are 48.
Hence the no. of small cubes with two faces coloured =48×2=96
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