Three metallic cubes whose edges are 3 cm, 4 cm and 5 cm, are melted and recast into a single cube. Find the edge of the new cube formed.

Answer

To solve the problem of finding the edge of a new cube formed by melting three metallic cubes with edges of 3 cm, 4 cm, and 5 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Volume of Each Cube:**
- The volume \( V \) of a cube is given by the formula:
\[ V = \text{edge}^3 \]
- For the first cube (edge = 3 cm):
\[ V_1 = 3^3 = 27 \text{ cm}^3 \]
- For the second cube (edge = 4 cm):
\[ V_2 = 4^3 = 64 \text{ cm}^3 \]
- For the third cube (edge = 5 cm):
\[ V_3 = 5^3 = 125 \text{ cm}^3 \]

2. **Calculate the Total Volume:**
- Now, we add the volumes of the three cubes:
\[ V_{\text{total}} = V_1 + V_2 + V_3 = 27 + 64 + 125 \]
- Performing the addition:
\[ V_{\text{total}} = 216 \text{ cm}^3 \]

3. **Find the Edge of the New Cube:**
- The volume of the new cube formed is equal to the total volume calculated:
\[ V_{\text{new cube}} = 216 \text{ cm}^3 \]
- To find the edge \( a \) of the new cube, we use the volume formula for a cube:
\[ a^3 = V_{\text{new cube}} \]
- Therefore:
\[ a^3 = 216 \]
- Taking the cube root of both sides to find \( a \):
\[ a = \sqrt[3]{216} \]
- Calculating the cube root:
\[ a = 6 \text{ cm} \]

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

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