Three cubes of a metal whose edges are in the ratio 3: 4: 5, are melted and converted into a single cube whose diagonal is 12 3  . Find the edges of the three cubes.

# Three cubes of a metal whose edges are in the ratio 3: 4: 5, are melted and converted into a single cube whose diagonal is  . Find the edges of the three cubes.

1. A
6 units, 7 units and 8 units
2. B
6 units, 8 units and 10 units
3. C
5 units, 7 units and 9 units
4. D
5 units, 6 units and 7 units

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### Solution:

Given that three cubes of a metal whose edges are in the ratio 3: 4: 5, are melted and converted into a single cube whose diagonal is  .
Let the three cubes of metals be 3x, 4x and 5x.
Volume of cube = (side)3
Now, according to the problem, this cubes are melted to form a single cube.
Then the volume of new cube = (33+43+53)x3.
⇒ Volume = (27+64+125)x3
⇒ Volume = 216x3
⇒ Volume = (6x)3
Then the side of the new cube is 6x.
The diagonal of a cube is given by   where a is the side of the cube.
We get,
Thus, the edges of the cubes are,
3x = 6 units
4x = 8 units
5x = 10 units
Hence, the edges of the cubes are 6 units, 8 units and 10 units.
Therefore, the correct answer is option (2).

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