A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The side of the cube is

Options

A. 6 cm
B. 8 cm
C. 12 cm
D. 24 cm

Answer

To find the side of the cube formed by melting a metal sheet, we need to follow these steps:

### Step 1: Calculate the Volume of the Metal Sheet
The volume of the metal sheet can be calculated using the formula for the volume of a rectangular prism, which is:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Thickness} \]

Given:
- Length = 27 cm
- Breadth = 8 cm
- Thickness = 1 cm

Substituting the values:
\[ \text{Volume} = 27 \, \text{cm} \times 8 \, \text{cm} \times 1 \, \text{cm} \]
\[ \text{Volume} = 216 \, \text{cm}^3 \]

### Step 2: Set the Volume of the Cube Equal to the Volume of the Metal Sheet
When the metal sheet is melted, it forms a cube with the same volume. Therefore, we have:
\[ \text{Volume of the cube} = 216 \, \text{cm}^3 \]

### Step 3: Use the Volume Formula for a Cube
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
where \( a \) is the length of a side of the cube.

### Step 4: Solve for the Side Length of the Cube
We can set the volume of the cube equal to the volume we calculated:
\[ a^3 = 216 \]

To find \( a \), we take the cube root of both sides:
\[ a = \sqrt[3]{216} \]

Calculating the cube root:
\[ a = 6 \, \text{cm} \]

### Final Answer
The side length of the cube is **6 cm**.

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