If the circumference of a circle is 352 metre, then its area in `m^2` is -----

Options

A. 9856
B. 8956
C. 6589
D. 5986

Answer

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

### Step 1: Understand the relationship between circumference and radius
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 into the formula
We know the circumference is 352 meters, so we can set up the equation:
\[ 352 = 2 \pi r \]

### Step 3: Solve for the radius \( r \)
To isolate \( r \), we first divide both sides by \( 2 \pi \):
\[ r = \frac{352}{2 \pi} \]
Using \( \pi \approx \frac{22}{7} \), we substitute this value into the equation:
\[ r = \frac{352}{2 \times \frac{22}{7}} = \frac{352 \times 7}{44} \]
Now, simplify the fraction:
\[ r = \frac{2464}{44} = 56 \text{ meters} \]

### Step 4: Calculate the area of the circle
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Substituting \( r = 56 \) meters into the area formula:
\[ A = \pi (56)^2 = \frac{22}{7} \times 3136 \]
Calculating \( 56^2 \):
\[ 56^2 = 3136 \]
Now substituting back:
\[ A = \frac{22 \times 3136}{7} \]
Calculating \( 22 \times 3136 \):
\[ 22 \times 3136 = 69092 \]
Now divide by 7:
\[ A = \frac{69092}{7} = 9870.285714285714 \approx 9880 \text{ m}^2 \]

### Final Answer:
The area of the circle is approximately \( 9880 \text{ m}^2 \).

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