A cube is painted in such a way that a pair of adjacent faces is painted in green; a pair of opposite faces is painted in yellow and another pair of adjacent faces is painted in red.This cube is now cut into 125 small but identical cubes. How many small cubes have at least two different colour on their faces?30383642
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Given : A cube is painted in such a way that a pair of adjacent faces is painted in green; a pair of opposite faces is painted in yellow and another pair of adjacent faces is painted in red.
cube is now cut into 125 small but identical cubes
To Find : How many small cubes have at least two different colours on their faces?
Solution:
Cube is cut in 125 = 5 * 5 * 5 cubes
Each side is cut in 5 parts
All corner cubes will have atleast different colours on their faces
= 8
Out of 12 Edges only two Edges will not have pair of different colors adjacent to them
10 Edges will have pair of different colors
Each edge will have 5- 2 = 3 cubes other than corners
10 * 3 = 30
30 + 8 = 38 small cubes have at least two different colours on their faces
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