The circumference of a circle is 88 cm. Find its area.

Options

A. `610cm^(2)`
B. `612cm^(2)`
C. `616cm^(2)`
D. `614cm^(2)`

Answer

To find the area of a circle when the circumference is given, 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:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

### Step 2: Substitute the given circumference into the formula.
We know that the circumference is 88 cm. So we can write:
\[ 2 \pi r = 88 \]

### Step 3: Solve for the radius (r).
To isolate \( r \), we can rearrange the equation:
\[ r = \frac{88}{2 \pi} \]
Now, substitute the value of \( \pi \) (approximately \( \frac{22}{7} \)):
\[ r = \frac{88}{2 \times \frac{22}{7}} \]
\[ r = \frac{88 \times 7}{2 \times 22} \]
\[ r = \frac{88 \times 7}{44} \]
Now simplify:
\[ r = \frac{616}{44} \]
\[ r = 14 \text{ cm} \]

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

### Step 5: Substitute the radius into the area formula.
Now that we have the radius, we can find the area:
\[ A = \pi (14)^2 \]
Substituting the value of \( \pi \):
\[ A = \frac{22}{7} \times 14 \times 14 \]

### Step 6: Calculate the area.
First, calculate \( 14 \times 14 \):
\[ 14 \times 14 = 196 \]
Now substitute it back into the area formula:
\[ A = \frac{22}{7} \times 196 \]
To simplify:
\[ A = \frac{22 \times 196}{7} \]
Now divide \( 196 \) by \( 7 \):
\[ 196 \div 7 = 28 \]
So now we have:
\[ A = 22 \times 28 \]
Calculating this gives:
\[ A = 616 \text{ cm}^2 \]

### Final Answer:
The area of the circle is \( 616 \text{ cm}^2 \).

---