Area of smallest square that can circumscribed circle of area `616 cm^2` is -----

Options

A. `784 cm^2`
B. `824cm^2`
C. `864 cm^2`
D. None of these

Answer

To find the area of the smallest square that can be circumscribed around a circle with an area of 616 cm², we can follow these steps:

### Step 1: Find the radius of the circle
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Given that the area of the circle is 616 cm², we can set up the equation:
\[ \pi r^2 = 616 \]

### Step 2: Solve for \( r^2 \)
To isolate \( r^2 \), we can divide both sides by \( \pi \):
\[ r^2 = \frac{616}{\pi} \]
Using \( \pi \approx \frac{22}{7} \) for calculation:
\[ r^2 = \frac{616 \times 7}{22} \]
Calculating this gives:
\[ r^2 = \frac{4312}{22} = 196 \]

### Step 3: Find the radius \( r \)
Now, we take the square root of \( r^2 \) to find the radius \( r \):
\[ r = \sqrt{196} = 14 \text{ cm} \]

### Step 4: Find the diameter of the circle
The diameter \( d \) of the circle is twice the radius:
\[ d = 2r = 2 \times 14 = 28 \text{ cm} \]

### Step 5: Find the side length of the circumscribed square
The side length \( s \) of the square that can circumscribe the circle is equal to the diameter of the circle:
\[ s = d = 28 \text{ cm} \]

### Step 6: Calculate the area of the square
The area \( A_s \) of the square is given by:
\[ A_s = s^2 = 28^2 = 784 \text{ cm}^2 \]

Thus, the area of the smallest square that can be circumscribed around the circle is:
\[ \boxed{784 \text{ cm}^2} \]