A metallic cuboid measuring 12 cm x 9 cm x 2 cm is melted and cast into a cube. Find the length of each edge of the cube.

Options

A. `5 cm`
B. `6 cm`
C. `2 cm`
D. `8 cm`

Answer

To solve the problem, we need to find the length of each edge of the cube formed by melting the metallic cuboid. Here are the steps to solve the problem:

### Step 1: Calculate the Volume of the Cuboid
The volume \( V \) of a cuboid can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given the dimensions of the cuboid are 12 cm, 9 cm, and 2 cm, we can substitute these values into the formula:
\[ V = 12 \, \text{cm} \times 9 \, \text{cm} \times 2 \, \text{cm} \]

### Step 2: Perform the Multiplication
Now, we perform the multiplication:
\[ V = 12 \times 9 = 108 \, \text{cm}^2 \]
Then, multiply by the height:
\[ V = 108 \times 2 = 216 \, \text{cm}^3 \]
So, the volume of the cuboid is \( 216 \, \text{cm}^3 \).

### Step 3: Set Up the Volume of the Cube
Let the length of each edge of the cube be \( x \) cm. The volume \( V \) of a cube is given by:
\[ V = x^3 \]
Since the volume of the cuboid is equal to the volume of the cube, we can set up the equation:
\[ x^3 = 216 \]

### Step 4: Solve for \( x \)
To find \( x \), we take the cube root of both sides:
\[ x = \sqrt[3]{216} \]

### Step 5: Calculate the Cube Root
Now we calculate the cube root of 216. We know that:
\[ 6 \times 6 \times 6 = 216 \]
Thus, \( x = 6 \).

### Conclusion
The length of each edge of the cube is \( 6 \, \text{cm} \).

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