If the circumference of a circle is 704 cm, then its area is :

Options

A. `49324 m^(2) `
B. `39424 m^(2) `
C. `3672 cm^(2) `
D. `39424 cm^(2) `

Answer

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

### Step 1: Write down 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 are given that the circumference is 704 cm. Therefore, we can write:
\[ 704 = 2\pi r \]

### Step 3: Solve for the radius \( r \).
To find \( r \), we can rearrange the equation:
\[ r = \frac{704}{2\pi} \]
Using \( \pi \approx \frac{22}{7} \), we can substitute this value in:
\[ r = \frac{704}{2 \times \frac{22}{7}} \]
\[ r = \frac{704 \times 7}{2 \times 22} \]
\[ r = \frac{704 \times 7}{44} \]
\[ r = \frac{4928}{44} \]
Now, simplifying \( \frac{4928}{44} \):
\[ r = 112 \text{ cm} \]

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

### Step 5: Substitute the radius into the area formula.
Now that we have the radius, we can find the area:
\[ A = \pi (112)^2 \]
Using \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times (112)^2 \]
Calculating \( (112)^2 \):
\[ (112)^2 = 12544 \]
Thus,
\[ A = \frac{22}{7} \times 12544 \]

### Step 6: Simplify the area calculation.
To simplify:
\[ A = \frac{22 \times 12544}{7} \]
Now, we can divide \( 12544 \) by \( 7 \):
\[ 12544 \div 7 = 1792 \]
So,
\[ A = 22 \times 1792 \]
Calculating this gives:
\[ A = 39304 \text{ cm}^2 \]

### Final Answer:
The area of the circle is \( 39,424 \text{ cm}^2 \).

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