A metal cube of edge 12cm is melted and formed into three smaller cubes. If the edges of the two smaller cubes are 6cm and 8cm, find the edge of the third smaller cube.

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the Volume of the Original Cube
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
where \( a \) is the edge length of the cube. For the original cube with an edge of 12 cm:
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