The area of a circular plot is 3850 square metres. What is the circumference of the plot?

Answer

To find the circumference of a circular plot given its area, we can follow these steps:

### Step 1: Write down the formula for the area of a circle.
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

### Step 2: Substitute the given area into the formula.
We know the area of the circular plot is 3850 square meters. So we can write:
\[ \pi r^2 = 3850 \]

### Step 3: Use the value of \( \pi \).
For calculations, we can use \( \pi \approx \frac{22}{7} \). Thus, we substitute this value into the equation:
\[ \frac{22}{7} r^2 = 3850 \]

### Step 4: Rearrange the equation to solve for \( r^2 \).
To isolate \( r^2 \), we multiply both sides by \( \frac{7}{22} \):
\[ r^2 = 3850 \times \frac{7}{22} \]

### Step 5: Calculate \( r^2 \).
Now we perform the multiplication:
\[ r^2 = 3850 \times \frac{7}{22} \]
Calculating this gives:
\[ r^2 = 3850 \times 0.31818 \approx 125 \text{ square meters} \]

### Step 6: Find the radius \( r \).
To find \( r \), we take the square root of \( r^2 \):
\[ r = \sqrt{125} \]
Calculating this gives:
\[ r = 11.18 \text{ meters} \]

### Step 7: Write down the formula for the circumference of a circle.
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]

### Step 8: Substitute the value of \( r \) into the circumference formula.
Using \( \pi \approx \frac{22}{7} \) and \( r \approx 11.18 \):
\[ C = 2 \times \frac{22}{7} \times 11.18 \]

### Step 9: Calculate the circumference.
Now we calculate:
\[ C = \frac{44}{7} \times 11.18 \]
Performing the multiplication gives:
\[ C \approx 220 \text{ meters} \]

### Final Answer:
The circumference of the circular plot is approximately **220 meters**.

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