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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
32
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B
28
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C
30
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D
18
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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

2028835_1961367_ans_b8e95700a45341a7ba49c8c6584924fd.jpg

Mathematics

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