The circumference of the circle is 176m. Then the area of the circle is:-

Options

A. a. 2464m^2
B. b. 2164m^2
C. c. 2346m^2
D. d. 2246m^2

Answer

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

### Step 1: Use the formula for the circumference of a circle.
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 that the circumference \( C \) is 176 m, so we can set up the equation:
\[ 176 = 2 \pi r \]

### Step 3: Solve for the radius \( r \).
To find \( r \), we can rearrange the equation:
\[ r = \frac{176}{2 \pi} \]
Now, simplify \( \frac{176}{2} \):
\[ r = \frac{88}{\pi} \]

### Step 4: Use the value of \( \pi \).
For calculations, we can use \( \pi \approx \frac{22}{7} \):
\[ r = \frac{88}{\frac{22}{7}} = 88 \times \frac{7}{22} \]
Now, simplify:
\[ r = 88 \div 22 \times 7 = 4 \times 7 = 28 \text{ m} \]

### Step 5: Calculate the area of the circle.
The formula for the area \( A \) of a circle is:
\[ A = \pi r^2 \]
Substituting the value of \( r \):
\[ A = \pi (28)^2 \]
Now, substituting \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times 28^2 \]
Calculating \( 28^2 \):
\[ 28^2 = 784 \]
So,
\[ A = \frac{22}{7} \times 784 \]

### Step 6: Simplify the area calculation.
We can simplify \( \frac{784}{7} \):
\[ 784 \div 7 = 112 \]
Thus,
\[ A = 22 \times 112 \]
Now, calculate:
\[ A = 2464 \text{ m}^2 \]

### Final Answer:
The area of the circle is \( 2464 \text{ m}^2 \).

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