A field is in the form of a circle. The cost of fencing around it at Rs. 12 per metre is Rs. 2,640. Whatis the area (in m ) of the field? (Take `pi=(22)/(7)` )

Options

A. `1925" m"^(2)`
B. `3850" m"^(2)`
C. `2772" m"^(2)`
D. `5544" m"^(2)`

Answer

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

### Step 1: Determine the total length of the fencing
The cost of fencing is given as Rs. 2,640, and the cost per meter is Rs. 12. To find the total length of the fencing (which is the circumference of the circle), we can use the formula:

\[ \text{Total length of fencing} = \frac{\text{Total cost}}{\text{Cost per meter}} = \frac{2640}{12} \]

### Step 2: Calculate the total length of fencing
Now, let's calculate:

\[ \frac{2640}{12} = 220 \text{ meters} \]

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

\[ C = 2 \pi r \]

Where \(r\) is the radius. We can substitute the value of \(C\) we found:

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

### Step 4: Solve for the radius \(r\)
Now, we can solve for \(r\):

\[ 220 = \frac{44}{7} \times r \]

Multiplying both sides by \(\frac{7}{44}\):

\[ r = 220 \times \frac{7}{44} \]

### Step 5: Simplify the expression for \(r\)
Calculating the right side:

\[ r = 220 \times \frac{7}{44} = 220 \div 44 \times 7 = 5 \times 7 = 35 \text{ meters} \]

### Step 6: Calculate the area of the circle
The area \(A\) of a circle is given by the formula:

\[ A = \pi r^2 \]

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

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

### Step 7: Calculate \(35^2\)
Calculating \(35^2\):

\[ 35^2 = 1225 \]

### Step 8: Calculate the area \(A\)
Now substituting back to find the area:

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

### Step 9: Simplify the area calculation
Calculating:

\[ A = \frac{22 \times 1225}{7} = 22 \times 175 = 3850 \text{ m}^2 \]

### Final Answer
Thus, the area of the field is:

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

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