Three cubes of metal whose edges are in the ratio 3:4:5 are melted down into a single cube whose diagonal is `12sqrt(3)\ c m` . Find the edges of three cubes.

Explanation

To find the edges of the three cubes of metal whose edges are in the ratio 3:4:5 and which are melted down into a single cube with a diagonal of \(12\sqrt{3}\) cm, we can follow these steps:

### Step 1: Define the edges of the cubes
Let the edges of the three cubes be \(3x\), \(4x\), and \(5x\) respectively, where \(x\) is a common multiplier.

### Step 2: Calculate the volume of each cube
The volume of a cube is given by the formula \(V = \text{edge}^3\). Therefore, the volumes of the three cubes are:
- Volume of the first cube: \((3x)^3 = 27x^3\)
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