One cubic metre of copper is melted and recast into a square cross - section bar 36 m long. An exact cube is cut off from this bar. If 1 cubic metre of copper costs Rs. 108, then the cost of this cube is

Options

A. 50 paise
B. 75 paise
C. One rupees
D. `1.50` rupees

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the problem
We have 1 cubic meter of copper that is recast into a bar with a square cross-section and a length of 36 meters. We need to find the cost of a cube that is cut from this bar.

### Step 2: Determine the volume of the bar
The volume of the bar is given as 1 cubic meter. Since the volume of a rectangular prism (or bar) is calculated as:
\[ \text{Volume} = \text{Length} \times \text{Area of Cross-section} \]

Let the area of the square cross-section be \( A \). The length of the bar is 36 meters. Thus, we can write:
\[ 1 = 36 \times A \]

### Step 3: Solve for the area of the square cross-section
Rearranging the equation gives:
\[ A = \frac{1}{36} \, \text{m}^2 \]

### Step 4: Find the side length of the square cross-section
Since the area \( A \) of a square is given by \( A = \text{side}^2 \), we can find the side length \( a \):
\[ a^2 = \frac{1}{36} \]
Taking the square root of both sides:
\[ a = \frac{1}{6} \, \text{m} \]

### Step 5: Determine the volume of the cube cut from the bar
The volume of a cube is given by:
\[ \text{Volume of cube} = \text{side}^3 \]
Substituting the side length:
\[ \text{Volume of cube} = \left(\frac{1}{6}\right)^3 = \frac{1}{216} \, \text{m}^3 \]

### Step 6: Calculate the cost of the cube
We know the cost of 1 cubic meter of copper is Rs. 108. Therefore, the cost of the cube is:
\[ \text{Cost of cube} = \text{Volume of cube} \times \text{Cost per cubic meter} \]
\[ \text{Cost of cube} = \frac{1}{216} \times 108 \]

### Step 7: Simplify the cost calculation
Calculating the cost:
\[ \text{Cost of cube} = \frac{108}{216} = \frac{1}{2} = 0.50 \, \text{Rs} \]

### Final Answer
The cost of the cube is Rs. 0.50.

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