Cost of erecting a fence round a square field of 625 hectares at 15 paise per metre is

Options

A. Rs. 500
B. Rs. 750
C. Rs. 100
D. Rs. 1500

Answer

To solve the problem of calculating the cost of erecting a fence around a square field of 625 hectares at 15 paise per meter, we will follow these steps:

### Step 1: Convert hectares to square meters
1 hectare is equal to \(10^4\) square meters. Therefore, to convert 625 hectares to square meters:
\[ 625 \text{ hectares} = 625 \times 10^4 \text{ m}^2 = 6250000 \text{ m}^2 \]

### Step 2: Find the side length of the square field
Since the area of a square is given by the formula \( \text{Area} = \text{side}^2 \), we can find the side length by taking the square root of the area:
\[ \text{side} = \sqrt{6250000} = 2500 \text{ m} \]

### Step 3: Calculate the perimeter of the square field
The perimeter \(P\) of a square is given by the formula:
\[ P = 4 \times \text{side} \]
Substituting the side length we found:
\[ P = 4 \times 2500 = 10000 \text{ m} \]

### Step 4: Calculate the total cost of fencing
The cost of fencing per meter is given as 15 paise, which is equivalent to \( \frac{15}{100} \) rupees. Therefore, the total cost \(C\) for the entire perimeter is:
\[ C = \text{Perimeter} \times \text{Cost per meter} = 10000 \text{ m} \times \frac{15}{100} \text{ rupees/m} \]
Calculating this gives:
\[ C = 10000 \times 0.15 = 1500 \text{ rupees} \]

### Final Answer
The cost of erecting a fence around the square field is **1500 rupees**.

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