The circumference of a circular sheet is 154 m. The area of the sheet is equal to

Options

A. ` 1886.5m^(2)`
B. ` 1806.5 m^(2)`
C. ` 1886.5 m^(2)`
D. ` 1688.5m^(2)`

Answer

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

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

### Step 2: Substitute the given circumference into the formula.
We know that the circumference is 154 m, so we can set up the equation:
\[ 154 = 2\pi r \]

### Step 3: Solve for the radius \( r \).
To find \( r \), we can rearrange the equation:
\[ r = \frac{154}{2\pi} \]
Now, substituting \( \pi \) with \( \frac{22}{7} \) for easier calculation:
\[ r = \frac{154}{2 \times \frac{22}{7}} = \frac{154 \times 7}{44} \]
Calculating the numerator:
\[ 154 \times 7 = 1078 \]
Now divide by 44:
\[ r = \frac{1078}{44} = 24.5 \text{ m} \]

### Step 4: Write down the formula for the area of a circle.
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]

### Step 5: Substitute the value of \( r \) into the area formula.
Now substituting \( r = 24.5 \) m into the area formula:
\[ A = \pi (24.5)^2 \]
Calculating \( (24.5)^2 \):
\[ (24.5)^2 = 600.25 \]
So,
\[ A = \pi \times 600.25 \]
Using \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times 600.25 \]

### Step 6: Calculate the area.
Calculating:
\[ A \approx \frac{22 \times 600.25}{7} = \frac{13205.5}{7} \approx 1886.5 \text{ m}^2 \]

### Final Answer:
The area of the circular sheet is approximately:
\[ \boxed{1886.5 \text{ m}^2} \]