.a cube 5x5x5 is given which is colored red. now it has been cut into 1x1x1 size .find out the no. of cubes having 2 faces colored.
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Best way to answer this question is to visualise the cube.
In the 5x5x5 cube, we will be considering only the 1x1x1 cubes that will be made using one of the edges of the bigger cube. This is so because it is obvious that any small cube made from the inside portion would have only one side painted.
Along the edges, the small cubes at the extreme corners can be discarded too as they would have 3 colored faces.
What is left is the middle cubes along the edges.
Total number of edges = 12.
No. of middle cubes in each = 3.
Therefore total number of cubes with two colored faces = 12x3 = 36
In the 5x5x5 cube, we will be considering only the 1x1x1 cubes that will be made using one of the edges of the bigger cube. This is so because it is obvious that any small cube made from the inside portion would have only one side painted.
Along the edges, the small cubes at the extreme corners can be discarded too as they would have 3 colored faces.
What is left is the middle cubes along the edges.
Total number of edges = 12.
No. of middle cubes in each = 3.
Therefore total number of cubes with two colored faces = 12x3 = 36
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Solution -
A cube with 5×5×5 is painted red and then it has been cut into 1×1×1 size. We have to find out the number of cubes having only 2 faces painted red.
It is very well known that only the cubes at the edge of the bigger cube can have two faces painted red.
The larger cube has each edge of 5 cm and smaller cube has each edge of 1 cm. Hence, there are 5 cubes on each edge. However, we need to consider 3 middle cubes only, as the 2 on each corner will have 3 painted faces.
Hence, there are 3 such cubes on each edge. As there are 12 edges in a cube. So, the total number of cubes having 2 faces painted red will be 12 × 3 = 36
So, 36 faces will be having red colour painted.
A cube with 5×5×5 is painted red and then it has been cut into 1×1×1 size. We have to find out the number of cubes having only 2 faces painted red.
It is very well known that only the cubes at the edge of the bigger cube can have two faces painted red.
The larger cube has each edge of 5 cm and smaller cube has each edge of 1 cm. Hence, there are 5 cubes on each edge. However, we need to consider 3 middle cubes only, as the 2 on each corner will have 3 painted faces.
Hence, there are 3 such cubes on each edge. As there are 12 edges in a cube. So, the total number of cubes having 2 faces painted red will be 12 × 3 = 36
So, 36 faces will be having red colour painted.
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