What would be the circumference of a circle whose area is 745.36 sq cm?

Options

A. 94.4cm
B. 88.8cm
C. 96.8cm
D. 87.4cm

Explanation

To find the circumference of a circle whose area is given as 745.36 sq cm, we can follow these steps:

### Step 1: Understand the formula for the area of a circle.
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

### Step 2: Substitute the given area into the formula.
We know the area \( A = 745.36 \) sq cm. Therefore, we can write:
\[ \pi r^2 = 745.36 \]

### Step 3: Use the value of \( \pi \).
For this calculation, we will use \( \pi \approx \frac{22}{7} \). Substituting this into the equation gives:
\[ \frac{22}{7} r^2 = 745.36 \]

### Step 4: Solve for \( r^2 \).
To isolate \( r^2 \), we multiply both sides by \( \frac{7}{22} \):
\[ r^2 = 745.36 \times \frac{7}{22} \]

### Step 5: Calculate \( r^2 \).
Now, we perform the multiplication:
\[ r^2 = 745.36 \times \frac{7}{22} = 237.16 \]

### Step 6: Find the radius \( r \).
To find \( r \), we take the square root of \( r^2 \):
\[ r = \sqrt{237.16} \approx 15.4 \text{ cm} \]

### Step 7: Calculate the circumference.
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
Substituting the values we have:
\[ C = 2 \times \frac{22}{7} \times 15.4 \]

### Step 8: Perform the calculation for circumference.
Calculating this gives:
\[ C = 2 \times \frac{22}{7} \times 15.4 \approx 96.8 \text{ cm} \]

### Final Answer:
The circumference of the circle is approximately \( 96.8 \) cm.

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