The cost of fencing a circular field at the rate of Rs 25 per meter is Rs 5,275 . Find the diameter of the field.

Answer

To find the diameter of the circular field based on the given cost of fencing, we can follow these steps:

### Step 1: Determine the total length of fencing
The total cost of fencing is given as Rs 5,275, and the cost per meter is Rs 25. To find the total length of fencing (which is the circumference of the circular field), we can use the formula:

\[ \text{Total Length (Circumference)} = \frac{\text{Total Cost}}{\text{Cost per meter}} \]

Substituting the values:

\[ \text{Circumference} = \frac{5275}{25} \]

### Step 2: Calculate the circumference
Now, we calculate the circumference:

\[ \text{Circumference} = 211 \text{ meters} \]

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

\[ C = 2\pi r \]

Where \(r\) is the radius. We can rearrange this formula to solve for \(r\):

\[ r = \frac{C}{2\pi} \]

Substituting the value of the circumference:

\[ r = \frac{211}{2\pi} \]

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

\[ r = \frac{211}{2 \times \frac{22}{7}} = \frac{211 \times 7}{44} = \frac{1477}{44} \text{ meters} \]

### Step 4: Calculate the diameter
The diameter \(d\) of the circle is twice the radius:

\[ d = 2r \]

Substituting the value of \(r\):

\[ d = 2 \times \frac{1477}{44} = \frac{2954}{44} \text{ meters} \]

### Step 5: Simplify the diameter
Now, we simplify \(\frac{2954}{44}\):

\[ d = 67.5 \text{ meters} \]

### Final Answer
Thus, the diameter of the circular field is **67.5 meters**.

---