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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 have at least one face coloured pink?
- a)1
- b)9
- c)16
- d)25
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A cube is coloured orange on one face, pink on the opposite face, brow...
If the cube is cut into 125 smaller cubes, how are the cuts made? 4 cuts/slices in x, y, z– planes respectively. So the cube is a 5 × 5 × 5 cube. That is, it has 5 squares on each of its faces.
So if only one face is painted pink, how many cubes have at least 1 face colored in pink? It is the number of cubes with only one side colored in pink because pink is only colored on one face. So, the answer would be: 5 ∗ 5=25
So if only one face is painted pink, how many cubes have at least 1 face colored in pink? It is the number of cubes with only one side colored in pink because pink is only colored on one face. So, the answer would be: 5 ∗ 5=25
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A cube is coloured orange on one face, pink on the opposite face, brow...
To determine the number of cubes that have at least one face colored pink, we need to consider the different orientations of the larger cube when it is cut into smaller cubes.
Let's analyze the given information step by step:
1. The cube is colored orange on one face and pink on the opposite face:
- This means that there are two cubes, one on each end of the cube, that have one face colored pink.
2. The cube is also colored brown on one face and silver on a face adjacent to the brown face:
- Since the cube has six faces, and two of them are already colored (orange and pink), we are left with four faces.
- Among these four faces, there are two adjacent faces to the brown face.
- One of these two adjacent faces is colored silver.
- Therefore, there are two cubes that have one face colored silver.
3. The other two faces are left uncolored:
- These two uncolored faces can be oriented in different ways when the cube is cut into smaller cubes.
- Let's consider the possible orientations:
- If both uncolored faces are adjacent to each other, there will be 1 cube with one face colored pink.
- If the two uncolored faces are opposite to each other, there will be 4 cubes with one face colored pink.
- If the two uncolored faces are adjacent to the orange face, there will be 4 cubes with one face colored pink.
- If the two uncolored faces are adjacent to the silver face, there will be 4 cubes with one face colored pink.
4. Calculating the total number of cubes with at least one face colored pink:
- Adding up all the cubes from the previous steps, we have:
- 2 cubes with one face colored pink from step 1.
- 2 cubes with one face colored silver from step 2.
- 1 cube with one face colored pink from the first orientation in step 3.
- 4 cubes with one face colored pink from the second orientation in step 3.
- 4 cubes with one face colored pink from the third orientation in step 3.
- 4 cubes with one face colored pink from the fourth orientation in step 3.
- Adding these numbers together, we get:
2 + 2 + 1 + 4 + 4 + 4 = 17
Therefore, there are 17 cubes with at least one face colored pink. However, the given options only include integers, so the closest option is 25 (option D).
Let's analyze the given information step by step:
1. The cube is colored orange on one face and pink on the opposite face:
- This means that there are two cubes, one on each end of the cube, that have one face colored pink.
2. The cube is also colored brown on one face and silver on a face adjacent to the brown face:
- Since the cube has six faces, and two of them are already colored (orange and pink), we are left with four faces.
- Among these four faces, there are two adjacent faces to the brown face.
- One of these two adjacent faces is colored silver.
- Therefore, there are two cubes that have one face colored silver.
3. The other two faces are left uncolored:
- These two uncolored faces can be oriented in different ways when the cube is cut into smaller cubes.
- Let's consider the possible orientations:
- If both uncolored faces are adjacent to each other, there will be 1 cube with one face colored pink.
- If the two uncolored faces are opposite to each other, there will be 4 cubes with one face colored pink.
- If the two uncolored faces are adjacent to the orange face, there will be 4 cubes with one face colored pink.
- If the two uncolored faces are adjacent to the silver face, there will be 4 cubes with one face colored pink.
4. Calculating the total number of cubes with at least one face colored pink:
- Adding up all the cubes from the previous steps, we have:
- 2 cubes with one face colored pink from step 1.
- 2 cubes with one face colored silver from step 2.
- 1 cube with one face colored pink from the first orientation in step 3.
- 4 cubes with one face colored pink from the second orientation in step 3.
- 4 cubes with one face colored pink from the third orientation in step 3.
- 4 cubes with one face colored pink from the fourth orientation in step 3.
- Adding these numbers together, we get:
2 + 2 + 1 + 4 + 4 + 4 = 17
Therefore, there are 17 cubes with at least one face colored pink. However, the given options only include integers, so the closest option is 25 (option D).
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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 have at least one face coloured pink?a)1b)9c)16d)25Correct 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 have at least one face coloured pink?a)1b)9c)16d)25Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 8.
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