The cost of fencing a circular field at the rate of Rs 12 meter is Rs 2640. The field is to be ploughed at the rate of Rs 0.50 per `m^(2)`. Find the cost of ploughing the field ( `pi = ( 22)/( 7))`

Answer

To solve the problem step by step, let's follow the reasoning laid out in the video transcript.

### Step 1: Find the circumference of the circular field.
The cost of fencing the circular field is given as Rs 2640 at the rate of Rs 12 per meter.

Using the formula for the cost of fencing:
\[ \text{Cost} = \text{Rate} \times \text{Circumference} \]
We can express the circumference in terms of the radius \( r \):
\[ \text{Circumference} = 2 \pi r \]
Thus, we have:
\[ 2640 = 12 \times (2 \pi r) \]

### Step 2: Solve for the radius \( r \).
Rearranging the equation:
\[ 2 \pi r = \frac{2640}{12} \]
Calculating the right side:
\[ \frac{2640}{12} = 220 \]
So,
\[ 2 \pi r = 220 \]
Now, substituting \( \pi \) with \( \frac{22}{7} \):
\[ 2 \times \frac{22}{7} \times r = 220 \]
This simplifies to:
\[ \frac{44}{7} r = 220 \]
Multiplying both sides by \( \frac{7}{44} \):
\[ r = 220 \times \frac{7}{44} \]
Calculating \( r \):
\[ r = 220 \times \frac{7}{44} = 35 \text{ meters} \]

### Step 3: Find the area of the circular field.
Using the formula for the area of a circle:
\[ \text{Area} = \pi r^2 \]
Substituting \( r = 35 \) meters and \( \pi = \frac{22}{7} \):
\[ \text{Area} = \frac{22}{7} \times (35)^2 \]
Calculating \( (35)^2 \):
\[ (35)^2 = 1225 \]
Thus,
\[ \text{Area} = \frac{22}{7} \times 1225 \]
Calculating the area:
\[ \text{Area} = \frac{22 \times 1225}{7} = 22 \times 175 = 3850 \text{ m}^2 \]

### Step 4: Calculate the cost of ploughing the field.
The cost of ploughing is given at the rate of Rs 0.50 per square meter. Therefore:
\[ \text{Cost of ploughing} = \text{Area} \times \text{Rate} \]
Substituting the values:
\[ \text{Cost of ploughing} = 3850 \times 0.50 \]
Calculating the cost:
\[ \text{Cost of ploughing} = 1925 \text{ Rs} \]

### Final Answer:
The cost of ploughing the field is Rs 1925.

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