The area of a circular field is 2464 `m^(2)` . Find the cost of fencing it at the rate of Rs. 6.50 per metre .

Options

A. Rs. 2144.
B. Rs. 1144.
C. Rs. 1244.
D. Rs. 1844.

Answer

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

### Step 1: Use the formula for the area of a circle
The formula for the area \( A \) of a circle is given by:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

### Step 2: Substitute the given area into the formula
We know the area \( A = 2464 \, m^2 \). Therefore, we can set up the equation:
\[ 2464 = \pi r^2 \]

### Step 3: Use the value of \( \pi \)
For our calculations, we will use \( \pi \approx \frac{22}{7} \). Substituting this into the equation gives:
\[ 2464 = \frac{22}{7} r^2 \]

### Step 4: Solve for \( r^2 \)
To isolate \( r^2 \), we can multiply both sides by \( \frac{7}{22} \):
\[ r^2 = 2464 \times \frac{7}{22} \]

### Step 5: Calculate \( r^2 \)
Now, calculate \( 2464 \times \frac{7}{22} \):
\[ r^2 = 2464 \times \frac{7}{22} = 784 \]

### Step 6: Find the radius \( r \)
Now, take the square root of both sides to find \( r \):
\[ r = \sqrt{784} = 28 \, m \]

### Step 7: Calculate the perimeter of the circular field
The perimeter \( P \) (or circumference) of a circle is given by:
\[ P = 2\pi r \]
Substituting the value of \( r \):
\[ P = 2 \times \frac{22}{7} \times 28 \]

### Step 8: Simplify the perimeter calculation
Calculating this gives:
\[ P = 2 \times \frac{22 \times 28}{7} = 2 \times 88 = 176 \, m \]

### Step 9: Calculate the cost of fencing
The cost of fencing is given at the rate of Rs. 6.50 per meter. Therefore, the total cost \( C \) is:
\[ C = P \times \text{rate} = 176 \times 6.50 \]

### Step 10: Calculate the total cost
Now, calculate the cost:
\[ C = 176 \times 6.50 = 1144 \, \text{Rs} \]

### Final Answer
Thus, the cost of fencing the circular field is **Rs. 1144**.

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