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December 10, 2008

3d cube problem

A block of wood in rectangular form that is
4cm x 10cm x 11cm all surfaces of pink rose color.
If the block of wood is cut into 440 cubes of
1cm × 1cm x 1cm each, how many cubes would
have color pink rose?


yogesh said...

384 cubes with at least on side with color pink rose

Secret Squïrrel said...

Only cubes which are entirely internal to the block would have no pink on them. The block is 4 x 10 x 11cm so the size of the uncoloured "block" inside is 2 x 8 9cm. This equals 144 cubes. There are 440 cubes in total so 440 - 144 = 296 cubes will have at least one face coloured pink.

Specifically, there are:
8 corner cubes with 3 pink faces
76 edge cubes with 2 pink faces
212 face cubes with 1 pink face