What is the area of a circle with circumference 88 cm ?

Options

A. 616 sq cm
B. 546 sq cm
C. 600 sq cm
D. 615 sq cm

Answer

To find the area of a circle with a given circumference of 88 cm, we can follow these steps:

### Step 1: Write down the formula for circumference.
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 the circumference is 88 cm, so we can set up the equation:
\[ 2\pi r = 88 \]

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

Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{88}{2 \times \frac{22}{7}} \]
\[ r = \frac{88 \times 7}{44} \]
\[ r = \frac{616}{44} \]
\[ r = 14 \text{ cm} \]

### 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 \( r = 14 \text{ cm} \), we can find the area:
\[ A = \pi (14)^2 \]
\[ A = \pi \times 196 \]

Using \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times 196 \]

### Step 6: Simplify the area calculation.
First, simplify \( \frac{196}{7} \):
\[ 196 \div 7 = 28 \]
So, we have:
\[ A = 22 \times 28 \]
\[ A = 616 \text{ cm}^2 \]

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

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