The weight of a cubic metre of a certain metal is 480 kg. It is melted and then rolled into a square bar 4 m long. Now an exact cube is cut from it. Find the weight of the cube.

Options

A. 240 kg
B. 80 kg
C. 120 kg
D. 60 kg

Answer

To solve the problem step by step, we need to find the weight of the cube that is cut from the square bar made from the melted metal.

### Step 1: Calculate the volume of the square bar
The square bar is 4 meters long, and since it is a square bar, we need to find the cross-sectional area. Let's assume the side length of the square cross-section is \( a \).

The volume \( V \) of the square bar can be calculated using the formula:
\[ V = \text{Length} \times \text{Area of cross-section} = \text{Length} \times a^2 \]
Given that the length of the bar is 4 m, we have:
\[ V = 4 \times a^2 \]

### Step 2: Determine the volume of the metal used
Since the metal has a density of 480 kg/m³, the total weight of the metal can be calculated by multiplying the volume by the density. However, we need to find the volume of the square bar first.

### Step 3: Find the volume of the cube
An exact cube is cut from the square bar. Let the side length of the cube be \( b \). The volume of the cube is given by:
\[ V_{\text{cube}} = b^3 \]

### Step 4: Relate the volumes
Since the volume of the metal remains constant, the volume of the square bar must equal the volume of the cube plus any remaining volume (if any). However, for this problem, we will assume that the entire volume of the square bar is used to create the cube.

### Step 5: Calculate the weight of the cube
The weight of the cube can be calculated using the formula:
\[ \text{Weight} = \text{Volume} \times \text{Density} \]
Substituting the volume of the cube:
\[ \text{Weight}_{\text{cube}} = b^3 \times 480 \text{ kg/m}^3 \]

### Step 6: Find the dimensions of the cube
To find \( b \), we need to determine the cross-sectional area \( a^2 \) of the square bar. Since the problem does not specify the side length of the square bar, we can assume it is 1 m for simplicity. Thus:
\[ V = 4 \times 1^2 = 4 \text{ m}^3 \]

### Step 7: Calculate the weight of the cube
Now, since the total volume of the metal is 4 m³, the weight of the cube can be calculated as follows:
\[ \text{Weight of the cube} = \text{Volume of the cube} \times \text{Density} \]
Assuming we cut a cube of 1 m³ from the bar:
\[ \text{Weight of the cube} = 1 \text{ m}^3 \times 480 \text{ kg/m}^3 = 480 \text{ kg} \]

However, if we cut a smaller cube, we need to find the exact volume of the cube cut from the bar. If we assume the cube has a side length of 1 m:
\[ \text{Weight of the cube} = 1^3 \times 480 = 480 \text{ kg} \]

### Final Calculation
If we assume the cube is cut from the entire volume of the bar, then:
\[ \text{Weight of the cube} = \frac{480 \text{ kg}}{4} = 120 \text{ kg} \]

### Conclusion
The weight of the cube is **120 kg**.