Three metal cubes of sides 5 cm, 4 cm and 3 cm respectively are melted and recast into a new cube. The edge of the new cube so formed is ____ cm.

Answer

To find the edge of the new cube formed by melting three metal cubes with sides of 5 cm, 4 cm, and 3 cm, we will follow these steps:

### Step 1: Calculate the volume of each cube.
- **Volume of the first cube (V1)**:
\[ V1 = \text{side}^3 = 5^3 = 125 \text{ cm}^3 \]

- **Volume of the second cube (V2)**:
\[ V2 = \text{side}^3 = 4^3 = 64 \text{ cm}^3 \]

- **Volume of the third cube (V3)**:
\[ V3 = \text{side}^3 = 3^3 = 27 \text{ cm}^3 \]

### Step 2: Find the total volume of the new cube.
- **Total Volume (V)**:
\[ V = V1 + V2 + V3 = 125 + 64 + 27 \]
\[ V = 216 \text{ cm}^3 \]

### Step 3: Relate the total volume to the new cube's edge length.
Let the edge length of the new cube be \( A \). The volume of the new cube can be expressed as:
\[ V = A^3 \]
Thus, we have:
\[ A^3 = 216 \]

### Step 4: Calculate the edge length of the new cube.
To find \( A \), we take the cube root of both sides:
\[ A = \sqrt[3]{216} \]

### Step 5: Simplify the cube root.
We can factor 216 to find its cube root:
\[ 216 = 2^3 \times 3^3 \]
Taking the cube root:
\[ A = \sqrt[3]{2^3 \times 3^3} = 2 \times 3 = 6 \text{ cm} \]

### Final Answer:
The edge of the new cube is **6 cm**.

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