A field is in the form of a circle . The cost of plough the field at rupes 1.50 per `m^(2)` is rupes 5775 . The cost fencing the field at rupes 8.50 per m is

Options

A. rupes 1870
B. rupes 2870
C. rupes 1970
D. rupes 2970

Answer

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

### Step 1: Calculate the Area of the Circular Field
Given that the cost of ploughing the field is ₹1.50 per m² and the total cost is ₹5775, we can find the area of the field.

\[ \text{Area} = \frac{\text{Total Cost}}{\text{Cost per m²}} = \frac{5775}{1.50} \]

### Step 2: Perform the Division
Calculating the area:

\[ \text{Area} = \frac{5775}{1.50} = 3850 \, m² \]

### Step 3: Relate Area to Radius
The area of a circle is given by the formula:

\[ \text{Area} = \pi r^2 \]

Substituting the area we found:

\[ 3850 = \pi r^2 \]

Using \(\pi \approx \frac{22}{7}\):

\[ 3850 = \frac{22}{7} r^2 \]

### Step 4: Solve for \(r^2\)
To isolate \(r^2\), multiply both sides by \(\frac{7}{22}\):

\[ r^2 = 3850 \times \frac{7}{22} \]

### Step 5: Calculate \(r^2\)
Now, calculate \(r^2\):

\[ r^2 = 3850 \times \frac{7}{22} = 3850 \times 0.31818 \approx 1225 \]

### Step 6: Find \(r\)
Taking the square root to find \(r\):

\[ r = \sqrt{1225} = 35 \, m \]

### Step 7: Calculate the Perimeter
The perimeter (circumference) of the circular field is given by:

\[ \text{Perimeter} = 2\pi r \]

Substituting the value of \(r\):

\[ \text{Perimeter} = 2 \times \frac{22}{7} \times 35 \]

### Step 8: Calculate the Perimeter Value
Calculating the perimeter:

\[ \text{Perimeter} = 2 \times \frac{22}{7} \times 35 = \frac{1540}{7} \approx 220 \, m \]

### Step 9: Calculate the Cost of Fencing
The cost of fencing is given as ₹8.50 per meter. Therefore, the total cost for fencing is:

\[ \text{Cost of Fencing} = \text{Perimeter} \times \text{Cost per meter} = 220 \times 8.50 \]

### Step 10: Calculate the Total Cost
Calculating the total cost of fencing:

\[ \text{Cost of Fencing} = 220 \times 8.50 = 1870 \]

### Final Answer
The cost of fencing the field is ₹1870.

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