The area of a circular field is 124.74 hectares . The cost of fencing it at the rate of 80 paise per metre is :

Options

A. Rs. 3168
B. Rs. 1584
C. Rs. 1729
D. none of these

Answer

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

### Step 1: Convert hectares to square meters
The area of the circular field is given as 124.74 hectares. To convert hectares to square meters, we use the conversion factor:
1 hectare = 10,000 square meters.

\[ \text{Area in square meters} = 124.74 \text{ hectares} \times 10,000 \text{ m}^2/\text{hectare} = 1,247,400 \text{ m}^2 \]

### Step 2: Use the area formula to find the radius
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
We can rearrange this formula to solve for \( r^2 \):
\[ r^2 = \frac{A}{\pi} \]
Substituting the area we found and using \( \pi \approx \frac{22}{7} \):
\[ r^2 = \frac{1,247,400}{\frac{22}{7}} = 1,247,400 \times \frac{7}{22} \]
Calculating this gives:
\[ r^2 = \frac{8,731,800}{22} = 396,900 \]

### Step 3: Find the radius
To find the radius \( r \), we take the square root of \( r^2 \):
\[ r = \sqrt{396,900} = 630 \text{ meters} \]

### Step 4: Calculate the circumference of the circular field
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
Substituting the value of \( r \):
\[ C = 2 \times \frac{22}{7} \times 630 \]
Calculating this:
\[ C = 2 \times 22 \times 90 = 3960 \text{ meters} \]

### Step 5: Calculate the cost of fencing
The cost of fencing is given as 80 paise per meter. To convert this to rupees, we note that:
\[ 80 \text{ paise} = \frac{80}{100} \text{ rupees} = 0.8 \text{ rupees} \]
Now, we calculate the total cost:
\[ \text{Total cost} = \text{Cost per meter} \times \text{Circumference} = 0.8 \times 3960 \]
Calculating this gives:
\[ \text{Total cost} = 3168 \text{ rupees} \]

### Final Answer
The total cost of fencing the circular field is **Rs 3168**.

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