If 88 m wire is required to fence of circular plot of land , then the area of the plot is -----

Options

A. `526 m^2`
B. `556 m^2`
C. `616 m^2`
D. None of these

Answer

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

### Step 1: Understand the relationship between circumference and radius
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

### Step 2: Substitute the given circumference
In this case, the circumference is given as 88 m. So we can set up the equation:
\[ 2\pi r = 88 \]

### Step 3: Solve for the radius \( r \)
To find the radius, we can rearrange the equation:
\[ r = \frac{88}{2\pi} \]
Now, calculate \( r \):
\[ r = \frac{88}{2 \times 3.14} \approx \frac{88}{6.28} \approx 14.0 \text{ m} \]

### Step 4: Calculate the area of the circle
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Substituting the value of \( r \):
\[ A = \pi (14.0)^2 \]
Calculating \( A \):
\[ A \approx 3.14 \times 196 \approx 615.44 \text{ m}^2 \]

### Step 5: Round the area to the nearest whole number
The area is approximately \( 615.44 \text{ m}^2 \), which can be rounded to:
\[ A \approx 616 \text{ m}^2 \]

### Final Answer
Thus, the area of the circular plot of land is approximately **616 m²**.

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