A solid cuboid with dimensions 18 cm `xx` 12 cm `xx` 8 cm is melted and turned into a cube. What is the length of its edge ?

Answer

To solve the problem of finding the length of the edge of a cube formed by melting a cuboid with dimensions 18 cm x 12 cm x 8 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Volume of the Cuboid:**
The volume \( V \) of a cuboid is given by the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
For our cuboid:
\[ V = 18 \, \text{cm} \times 12 \, \text{cm} \times 8 \, \text{cm} \]

2. **Perform the Multiplication:**
First, calculate \( 18 \times 12 \):
\[ 18 \times 12 = 216 \, \text{cm}^2 \]
Now multiply this result by 8:
\[ 216 \, \text{cm}^2 \times 8 \, \text{cm} = 1728 \, \text{cm}^3 \]
Thus, the volume of the cuboid is \( 1728 \, \text{cm}^3 \).

3. **Set the Volume of the Cube Equal to the Volume of the Cuboid:**
When the cuboid is melted and formed into a cube, the volume of the cube \( V \) is given by:
\[ V = a^3 \]
where \( a \) is the length of the edge of the cube. Therefore, we have:
\[ a^3 = 1728 \, \text{cm}^3 \]

4. **Calculate the Length of the Edge of the Cube:**
To find \( a \), we take the cube root of both sides:
\[ a = \sqrt[3]{1728} \]

5. **Finding the Cube Root:**
We can simplify \( 1728 \) by prime factorization:
\[ 1728 = 12^3 \]
Therefore:
\[ a = 12 \, \text{cm} \]

### Final Answer:
The length of the edge of the cube is \( 12 \, \text{cm} \).

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