What would be the area of a circle whose circumference is 35.2cm?

Options

A. 67.22 sq cm
B. 75.54 sq cm
C. 98.56 sq cm
D. 86.75 sq cm

Explanation

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

### Step 1: Understand the relationship between circumference and radius
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
We know the circumference \( C \) is 35.2 cm. So we can set up the equation:
\[ 2\pi r = 35.2 \]

### Step 3: Solve for the radius \( r \)
Using \( \pi \approx \frac{22}{7} \), we can rewrite the equation:
\[ 2 \times \frac{22}{7} \times r = 35.2 \]
Now, simplify the equation:
\[ \frac{44}{7} r = 35.2 \]
To isolate \( r \), multiply both sides by \( \frac{7}{44} \):
\[ r = 35.2 \times \frac{7}{44} \]
Calculating this gives:
\[ r = 35.2 \times 0.1591 \approx 5.6 \text{ cm} \]

### Step 4: Calculate the area of the circle
The formula for the area \( A \) of a circle is given by:
\[ A = \pi r^2 \]
Substituting \( r = 5.6 \) cm into the area formula:
\[ A = \frac{22}{7} \times (5.6)^2 \]
Calculating \( (5.6)^2 \):
\[ (5.6)^2 = 31.36 \]
Now substituting back into the area formula:
\[ A = \frac{22}{7} \times 31.36 \]
Calculating this gives:
\[ A \approx 98.56 \text{ cm}^2 \]

### Final Answer
The area of the circle is approximately \( 98.56 \text{ cm}^2 \).

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