Two faces each of a cube of side 6 cm have been painted blue, red and yellow. If it is cut into cubes of side 1 cm each, then how many small cubes will have ONLY ONE side painted either blue or red?
Answers
Given : Two faces each of a cube of side 6 cm have been painted blue, red and yellow. it is cut into cubes of side 1 cm each
To find : how many small cubes will have ONLY ONE side painted either blue or red?
Solution:
Number of cubes = 6 * 6 * 6 = 216
No Face colored cubes = 4 * 4 * 4 = 64 cubes
only one face colored cubes = 6 * 4 * 4 = 96 cubes
two face colored cubes = 48
3 faces colored cubes = 8
Only one side red cubes = 2 * 4 * 4 = 32 cubes
Only one side blue cubes = 2 * 4 * 4 = 32 cubes
Only one side yellow cubes = 2 * 4 * 4 = 32 cubes
Either Blue or Red = 32 + 32 = 64 cubes
64 small cubes have only one side painted either blue or red
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