A cube is painted red on all sides. If 3 cuts are made on its each face (equally spaced), then how many cubes will be obtained which have none of their faces coloured?
Answers
Answered by
1
Answer:
ANSWER
To cut it into 125 congruent smaller cubes required 5 horizontal cuts and 5 vertical cuts. The only cubes that are pointed red on one side are the interior cubes of each side of 25 cubes sides, 9 of them are painted red on only one side.
i.e, 9×6=54 cubes that are not painted at all are the interior cubes, there are 3×3×3=27 interior cubes.
Of all 125 cubes,
27 are interior cubes, that have no sides painted red.
54 are cubes painted on only one side.
36 are cubes that are painted red on two side.
8 are corner cubes, painted red on 3 sides.
Probability that 3 faces shows red color
⇒ The probability of red side facing up =
125
27
×
6
0
+
125
54
×
6
1
+
125
36
×
6
2
+
125
8
×
6
3
=
6
1
⇒ Probability of two more red colour facing up =
6
1
×
49
4×6
=
49
4
.
Hence, the answer is
49
4
.
Answered by
2
Answer:
8
Step-by-step explanation:
It's answer is 8 I m fully sure .
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