Chi S.

asked • 12/26/15

A cube painted yellow on all its faces then it is cut into 27 smaller cubes of identical size.how many are painted?

A cube painted yellow on all its faces then it is cut into 27 smaller cubes of identical size..How many small cubes are small cubes are painted on one face only?How many cubes are not painted on any faces?

2 Answers By Expert Tutors

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David W. answered • 12/27/15

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4.7 (80)

Experienced Prof

Mark M.

Adding the number of faces given in the last two sentences I get 55, not 27.
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12/27/15

David W.

tutor
The original cube has 6 sides which are cut so that each original side has 9 exposed faces of smaller cubes.  This means that 6*9=54 small faces (this not the number of small cubes) have paint.  Of the 27 (3*3*3) smaller cubes formed by the cutting, 1 gets no paint, 6 are painted on 1 face, 12 are painted on 2 faces, and 8 are painted on 3 faces (total 27 cubes).  The sum of the cubes in Marlene S.'s last two sentences is 27.  The sum of the painted faces (of the small cubes) is 54 (which is 6*9).
 
The problem statement, "how many are painted?" must mean "How many small cubes are painted?" and the statement.
statements, "How many small cubes are small cubes are painted on one face only?How many cubes are not painted on any faces?" has duplicated words, but asks about cubes, not faces.
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12/27/15

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