Cost of ploughing at the rate of Rs 10 per `m^(2)` is Rs 1540. Find the radius of circular field. `( pi = ( 22)/( 7))`

Answer

To find the radius of the circular field given the cost of ploughing, we can follow these steps:

### Step 1: Understand the given information
We know:
- Cost of ploughing per square meter = Rs 10
- Total cost of ploughing = Rs 1540

### Step 2: Calculate the area of the circular field
To find the area of the circular field, we can use the formula:
\[ \text{Area} = \frac{\text{Total Cost}}{\text{Cost per square meter}} \]
Substituting the values:
\[ \text{Area} = \frac{1540}{10} = 154 \, m^2 \]

### Step 3: Use the area to find the radius
The area \(A\) of a circle is given by the formula:
\[ A = \pi r^2 \]
Where \(\pi = \frac{22}{7}\). We can set this equal to the area we calculated:
\[ 154 = \frac{22}{7} r^2 \]

### Step 4: Solve for \(r^2\)
To isolate \(r^2\), multiply both sides by \(\frac{7}{22}\):
\[ r^2 = 154 \times \frac{7}{22} \]
Calculating the right side:
\[ r^2 = 154 \times \frac{7}{22} = 154 \times \frac{1}{3.14} \approx 49 \]

### Step 5: Calculate the radius \(r\)
Now, take the square root of both sides to find \(r\):
\[ r = \sqrt{49} = 7 \, m \]

### Conclusion
The radius of the circular field is \(7\) meters.

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