The circumference of circular field is 616 m then find out the area?

Options

A. `30080m^2`
B. `28226m^2`
C. `34184 m^2`
D. `30184 m^2`

Answer

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

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

### Step 2: Substitute the given circumference
We know the circumference is 616 m, so we can set up the equation:
\[ 616 = 2\pi r \]

### Step 3: Solve for the radius (r)
To find the radius, we can rearrange the equation:
\[ r = \frac{C}{2\pi} \]
Substituting \( C = 616 \) and using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{616}{2 \times \frac{22}{7}} \]

### Step 4: Simplify the expression
Calculating the denominator:
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
Now, substituting back:
\[ r = \frac{616 \times 7}{44} \]

### Step 5: Perform the multiplication and division
Calculating \( 616 \div 44 \):
\[ 616 \div 44 = 14 \]
So, we have:
\[ r = 14 \times 7 = 98 \text{ m} \]

### Step 6: Calculate the area (A) using the radius
The formula for the area (A) of a circle is:
\[ A = \pi r^2 \]
Substituting \( r = 98 \) and \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times (14)^2 \]

### Step 7: Calculate \( (14)^2 \)
Calculating \( (14)^2 \):
\[ (14)^2 = 196 \]
So, substituting back:
\[ A = \frac{22}{7} \times 196 \]

### Step 8: Simplify the area calculation
Calculating:
\[ A = \frac{22 \times 196}{7} \]
Calculating \( 196 \div 7 = 28 \):
\[ A = 22 \times 28 = 616 \text{ m}^2 \]

### Final Answer
Thus, the area of the circular field is:
\[ \text{Area} = 616 \text{ m}^2 \]

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