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A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.
How many cubes are coloured orange on one face and have the remaining faces uncoloured?
  • a)
    8
  • b)
    12
  • c)
    14
  • d)
    16
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A cube is coloured orange on one face, pink on the opposite face, brow...
Given: A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size.

To find: How many cubes are coloured orange on one face and have the remaining faces uncoloured?

Solution:

Number of smaller cubes obtained by cutting the larger cube = 125

Let's find the number of smaller cubes that have one face coloured orange.

The larger cube has 6 faces. One face is coloured orange.

When the larger cube is cut into smaller cubes, the cubes that have one face coloured orange will be those that have an orange face on any of the 6 faces of the larger cube.

Therefore, the number of smaller cubes that have one face coloured orange = number of cubes with an orange face on any of the 6 faces of the larger cube.

Number of cubes with an orange face on any of the 6 faces of the larger cube = number of cubes with an orange face that are present on the middle layer of the larger cube.

The larger cube has 5 layers of 25 smaller cubes each.

The middle layer is the third layer.

The third layer has the orange face on two opposite cubes.

Therefore, the number of smaller cubes with one face coloured orange = 2.

Answer: Option D) 16.
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Community Answer
A cube is coloured orange on one face, pink on the opposite face, brow...
Only one face colored.
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A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.How many cubes are coloured orange on one face and have the remaining faces uncoloured?a)8b)12c)14d)16Correct answer is option 'D'. Can you explain this answer?
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Solutions for A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.How many cubes are coloured orange on one face and have the remaining faces uncoloured?a)8b)12c)14d)16Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 8. Download more important topics, notes, lectures and mock test series for Class 8 Exam by signing up for free.
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