The cost of mowing a circular field at Rs. 16 per sq. m is Rs. 2464 field.
(i) The total area of the field.
(ii) The radius of the circular field
(iii) Cost of fencing the field at Rs. 12 per metre.

Answer

To solve the problem step by step, let's break it down into the three parts as given in the question.

### Step 1: Calculate the Total Area of the Field
The total area of the circular field can be calculated using the formula:

\[ \text{Total Area} = \frac{\text{Total Cost}}{\text{Cost per square meter}} \]

Given:
- Total Cost = Rs. 2464
- Cost per square meter = Rs. 16

Substituting the values:

\[ \text{Total Area} = \frac{2464}{16} \]

Calculating this gives:

\[ \text{Total Area} = 154 \text{ m}^2 \]

### Step 2: Calculate the Radius of the Circular Field
The area of a circle is given by the formula:

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

We have already calculated the area as 154 m². Using the value of \(\pi \approx \frac{22}{7}\):

\[ 154 = \frac{22}{7} r^2 \]

To find \(r^2\), we rearrange the equation:

\[ r^2 = \frac{154 \times 7}{22} \]

Calculating this gives:

\[ r^2 = \frac{1078}{22} = 49 \]

Taking the square root of both sides:

\[ r = \sqrt{49} = 7 \text{ m} \]

### Step 3: Calculate the Cost of Fencing the Field
The cost of fencing is based on the circumference of the circular field, which is given by the formula:

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

Substituting the value of \(r = 7\) m:

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

Calculating this gives:

\[ \text{Circumference} = 44 \text{ m} \]

Now, to find the cost of fencing, we multiply the circumference by the cost per meter:

\[ \text{Cost of Fencing} = \text{Circumference} \times \text{Cost per meter} \]

Given the cost per meter is Rs. 12:

\[ \text{Cost of Fencing} = 44 \times 12 = 528 \text{ Rs.} \]

### Summary of Results
1. Total Area of the field: **154 m²**
2. Radius of the circular field: **7 m**
3. Cost of fencing the field: **Rs. 528**