A field is in the form of a circle. The cost of fencing around it at Rs. 11 per metres is Rs.2,420.What is the area (in `m^(2)`) of the field ? (Take `pi=22/7`)

Options

A. 3850
B. 4500
C. 4250
D. 2700

Answer

To solve the problem, we need to find the area of a circular field given the cost of fencing around it. Here are the steps to solve the problem:

### Step 1: Calculate the total length of the fencing
The total cost of fencing is given as Rs. 2,420, and the cost per meter is Rs. 11. We can find the total length of the fencing (which is the circumference of the circle) using the formula:

\[ \text{Total Length} = \frac{\text{Total Cost}}{\text{Cost per meter}} = \frac{2420}{11} \]

### Step 2: Perform the division
Calculating the above expression:

\[ \text{Total Length} = \frac{2420}{11} = 220 \text{ meters} \]

### Step 3: Use the circumference to find the radius
The circumference \(C\) of a circle is given by the formula:

\[ C = 2\pi r \]

We can rearrange this formula to find the radius \(r\):

\[ r = \frac{C}{2\pi} \]

Substituting the value of \(C\) (220 meters) and \(\pi = \frac{22}{7}\):

\[ r = \frac{220}{2 \times \frac{22}{7}} = \frac{220 \times 7}{2 \times 22} \]

### Step 4: Simplify to find the radius
Calculating the above expression:

\[ r = \frac{220 \times 7}{44} = \frac{1540}{44} = 35 \text{ meters} \]

### Step 5: Calculate the area of the circle
The area \(A\) of a circle is given by the formula:

\[ A = \pi r^2 \]

Substituting the value of \(r\) and \(\pi\):

\[ A = \frac{22}{7} \times (35)^2 \]

### Step 6: Perform the calculation for the area
Calculating \(35^2\):

\[ 35^2 = 1225 \]

Now substituting back into the area formula:

\[ A = \frac{22}{7} \times 1225 \]

### Step 7: Simplify the area calculation
Calculating the area:

\[ A = \frac{22 \times 1225}{7} = \frac{26950}{7} = 3850 \text{ m}^2 \]

### Final Answer
The area of the field is:

\[ \boxed{3850 \text{ m}^2} \]

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