A field is in the form of a circle. The area of the field is `3850 m^(2)`, and if the cost of fencing around it is `Rs. 11` per metre, then the total cost (in `Rs.`) is:
(Take `pi=(22)/(7)`)

Options

A. 2200
B. 2420
C. 2840
D. 3000

Answer

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

### Step 1: Find the radius of the circular field using the area formula.
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
We know the area \( A = 3850 \, m^2 \) and we will use \( \pi = \frac{22}{7} \).

Substituting the values into the formula:
\[ 3850 = \frac{22}{7} r^2 \]

### Step 2: Rearrange the equation to solve for \( r^2 \).
To isolate \( r^2 \), we multiply both sides by \( \frac{7}{22} \):
\[ r^2 = 3850 \times \frac{7}{22} \]

### Step 3: Simplify the right side.
Calculating \( 3850 \times \frac{7}{22} \):
1. First, divide \( 3850 \) by \( 22 \):
\[ 3850 \div 22 = 175 \]
2. Then multiply by \( 7 \):
\[ 175 \times 7 = 1225 \]
So, we have:
\[ r^2 = 1225 \]

### Step 4: Find the radius \( r \).
Taking the square root of both sides:
\[ r = \sqrt{1225} = 35 \, m \]

### Step 5: Calculate the circumference of the circle.
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
Substituting the values:
\[ C = 2 \times \frac{22}{7} \times 35 \]

### Step 6: Simplify the circumference calculation.
1. First, calculate \( 2 \times 35 = 70 \).
2. Then, calculate \( C = \frac{22}{7} \times 70 \):
\[ C = 22 \times 10 = 220 \, m \]

### Step 7: Calculate the total cost of fencing.
The cost of fencing is given as \( Rs. 11 \) per meter. Therefore, the total cost \( T \) is:
\[ T = C \times \text{cost per meter} = 220 \times 11 \]

### Step 8: Perform the final multiplication.
Calculating \( 220 \times 11 \):
\[ T = 2420 \, Rs. \]

### Final Answer:
The total cost of fencing around the circular field is **Rs. 2420**.

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