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A cube of side 10 cm is coloured red, with a 2 cm wide green strip along all the sides on all the faces. The cube is cut into 125 smaller cubes of equal sizes. How many cubes have at least two green faces each?
- a)8
- b)27
- c)44
- d)63
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A cube of side 10 cm is coloured red, with a 2 cm wide green strip al...
Given:
- A cube of side 10 cm is coloured red, with a 2 cm wide green strip along all the sides on all the faces.
- The cube is cut into 125 smaller cubes of equal sizes.
To find:
- How many cubes have at least two green faces each?
Solution:
Number of smaller cubes inside the 10 cm cube = 125 (since it has been cut into 125 smaller cubes of equal sizes)
Each face of the larger cube has 5 x 5 = 25 smaller cubes. Out of these, the corner cubes have 3 faces painted green, the edge cubes have 2 faces painted green, and the remaining cubes have only one face painted green.
So, we need to count the number of corner cubes and edge cubes to get the total number of cubes that have at least two green faces each.
- Corner cubes: There are 8 corner cubes. Each corner cube has 3 faces painted green. Therefore, the total number of corner cubes that have at least two green faces each = 8 x 3 = 24.
- Edge cubes: There are 12 edge cubes along each edge of the larger cube. Each edge cube has 2 faces painted green. Therefore, the total number of edge cubes that have at least two green faces each = 12 x 6 x 2 = 144.
However, we need to remove the corner cubes from the total count of edge cubes because we have already counted them as corner cubes.
Therefore, the total number of cubes that have at least two green faces each = 144 - 24 = 120.
Answer:
Option (c) 44.
- A cube of side 10 cm is coloured red, with a 2 cm wide green strip along all the sides on all the faces.
- The cube is cut into 125 smaller cubes of equal sizes.
To find:
- How many cubes have at least two green faces each?
Solution:
Number of smaller cubes inside the 10 cm cube = 125 (since it has been cut into 125 smaller cubes of equal sizes)
Each face of the larger cube has 5 x 5 = 25 smaller cubes. Out of these, the corner cubes have 3 faces painted green, the edge cubes have 2 faces painted green, and the remaining cubes have only one face painted green.
So, we need to count the number of corner cubes and edge cubes to get the total number of cubes that have at least two green faces each.
- Corner cubes: There are 8 corner cubes. Each corner cube has 3 faces painted green. Therefore, the total number of corner cubes that have at least two green faces each = 8 x 3 = 24.
- Edge cubes: There are 12 edge cubes along each edge of the larger cube. Each edge cube has 2 faces painted green. Therefore, the total number of edge cubes that have at least two green faces each = 12 x 6 x 2 = 144.
However, we need to remove the corner cubes from the total count of edge cubes because we have already counted them as corner cubes.
Therefore, the total number of cubes that have at least two green faces each = 144 - 24 = 120.
Answer:
Option (c) 44.
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Community Answer
A cube of side 10 cm is coloured red, with a 2 cm wide green strip al...
There are 12 cubes in each of the layers 1 and 5 and 4 cubes in each of the layers 2, 3 and 4 which have two faces coloured green. Also, there are 4 cubes in each of the layers 1 and 5 which have three faces coloured green.
3 faces coloured cubes = 8
2 faces coloured cubes = 24 + 12 = 36
Total cubes = 44
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A cube of side 10 cm is coloured red, with a 2 cm wide green strip along all the sides on all the faces. The cube is cut into 125 smaller cubes of equal sizes. How many cubes have at least two green faces each?a)8b)27c)44d)63Correct answer is option 'C'. Can you explain this answer?
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