A circle is inscribed in a square and the area of square is 784 `cm^2`. Find the area of the circle.

Options

A. `154 cm^2`
B. `308 cm^2`
C. `616 cm^2`
D. `1232 cm^2`

Answer

To find the area of a circle inscribed in a square with a given area, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the area of the square**:
The area of the square is given as \( 784 \, \text{cm}^2 \).

2. **Find the side length of the square**:
The formula for the area of a square is:
\[ \text{Area} = \text{side}^2 \]
To find the side length, we take the square root of the area:
\[ \text{side} = \sqrt{784} = 28 \, \text{cm} \]

3. **Determine the diameter of the inscribed circle**:
The diameter of the inscribed circle is equal to the side length of the square. Therefore:
\[ \text{Diameter} = 28 \, \text{cm} \]

4. **Calculate the radius of the circle**:
The radius \( r \) is half of the diameter:
\[ r = \frac{\text{Diameter}}{2} = \frac{28}{2} = 14 \, \text{cm} \]

5. **Find the area of the circle**:
The formula for the area of a circle is:
\[ \text{Area} = \pi r^2 \]
Substituting the value of \( r \):
\[ \text{Area} = \pi (14)^2 = \pi \times 196 \]
Using \( \pi \approx \frac{22}{7} \):
\[ \text{Area} = \frac{22}{7} \times 196 \]

6. **Simplify the area calculation**:
First, simplify \( \frac{196}{7} \):
\[ \frac{196}{7} = 28 \]
Now, multiply by 22:
\[ \text{Area} = 22 \times 28 = 616 \, \text{cm}^2 \]

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