The area (in sq. cm.) of the largest circle that can be drawn inside a square of side 28 cm, is : 

Options

A. (a) 17248
B. (b) 784
C. (c) 8624
D. (d) 616

Answer

To find the area of the largest circle that can be drawn inside a square with a side length of 28 cm, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Diameter of the Circle**:
The largest circle that can fit inside a square will have a diameter equal to the side length of the square. Since the side of the square is 28 cm, the diameter of the circle is also 28 cm.
\[ \text{Diameter of the circle} = 28 \, \text{cm} \]

2. **Calculate the Radius of the Circle**:
The radius (r) of the circle is half of the diameter. Therefore, we can calculate the radius as follows:
\[ r = \frac{\text{Diameter}}{2} = \frac{28 \, \text{cm}}{2} = 14 \, \text{cm} \]

3. **Use the Area Formula for the Circle**:
The area (A) of a circle is given by the formula:
\[ A = \pi r^2 \]
Substituting the value of the radius:
\[ A = \pi (14 \, \text{cm})^2 \]

4. **Calculate the Area**:
Now, we can calculate the area using the value of π (approximately 3.14 or \(\frac{22}{7}\)):
\[ A = \pi \times 196 \, \text{cm}^2 \]
Using \(\frac{22}{7}\) for π:
\[ A = \frac{22}{7} \times 196 \]
To simplify this:
\[ A = \frac{22 \times 196}{7} \]
First, calculate \(196 \div 7 = 28\):
\[ A = 22 \times 28 \]
Now, calculate \(22 \times 28\):
\[ A = 616 \, \text{cm}^2 \]

5. **Conclusion**:
The area of the largest circle that can be drawn inside a square of side 28 cm is:
\[ \text{Area} = 616 \, \text{cm}^2 \]