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Question
A cube is coloured blue on one face, yellow on the opposite face, red on another face and green on a face adjacent to the red face. The other two faces are left uncoloured. It is then cut into 64 smaller cubes of equal size.
How many cubes are have only one face coloured ? [#9]
A cube is coloured blue on one face, yellow on the opposite face, red on another face and green on a face adjacent to the red face. The other two faces are left uncoloured. It is then cut into 64 smaller cubes of equal size.
How many cubes are have only one face coloured ? [#9]
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Solution
The correct option is C 30
Take a 4x4x4 cube
Paint Blue on bottom and red on top.
Red on left side and green on back
Ref figure.
cubes having only one face colour are in Row1 & Row 4 of column b, c, d, f, g, h, j, k, l = 2 x 9 = 18
cubes having only one face colour are in Row2 & Row3 of column a, e , i, n, o, p = 2x6 = 12
no of cube having only one face coloured = 18 + 12 = 30
Take a 4x4x4 cube
Paint Blue on bottom and red on top.
Red on left side and green on back
Ref figure.
cubes having only one face colour are in Row1 & Row 4 of column b, c, d, f, g, h, j, k, l = 2 x 9 = 18
cubes having only one face colour are in Row2 & Row3 of column a, e , i, n, o, p = 2x6 = 12
no of cube having only one face coloured = 18 + 12 = 30
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