A rectangular sheet of paper is 35 cm long and 28 cm wide. Find the area of the largest circle that can be cut from this sheet.

Answer

To find the area of the largest circle that can be cut from a rectangular sheet of paper measuring 35 cm long and 28 cm wide, we can follow these steps:

### Step-by-step Solution:

1. **Identify the dimensions of the rectangle**:
- Length = 35 cm
- Width = 28 cm

2. **Determine the diameter of the largest circle that can fit inside the rectangle**:
- The diameter of the circle must be equal to the smaller dimension of the rectangle.
- Compare the length and width: 28 cm (width) is smaller than 35 cm (length).
- Therefore, the diameter (d) of the circle is 28 cm.

3. **Calculate the radius of the circle**:
- The radius (r) is half of the diameter.
- \( r = \frac{d}{2} = \frac{28 \text{ cm}}{2} = 14 \text{ cm} \)

4. **Calculate the area of the circle**:
- The area (A) of a circle is given by the formula:
\[ A = \pi r^2 \]
- Substitute the value of the radius:
\[ A = \pi \times (14 \text{ cm})^2 \]
- Calculate \( (14 \text{ cm})^2 = 196 \text{ cm}^2 \):
\[ A = \pi \times 196 \text{ cm}^2 \]

5. **Use the value of π**:
- We can use \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times 196 \text{ cm}^2 \]

6. **Perform the multiplication**:
- First, simplify \( \frac{22 \times 196}{7} \):
- Calculate \( 22 \times 196 = 4312 \)
- Now divide by 7:
\[ A = \frac{4312}{7} \approx 616 \text{ cm}^2 \]

7. **Final answer**:
- The area of the largest circle that can be cut from the rectangular sheet is approximately \( 616 \text{ cm}^2 \).