From each of the four comers of a rectangular sheet of dimensions 48cm `xx` 27cm, a square of side 3.5 cm is cut off and a box is made. The volume of the box is:

Options

A. `2880cm^(3)`
B. `2780cm^(3)`
C. `2870cm^(3)`
D. `2860cm^(3)`

Answer

To solve the problem of finding the volume of the box created from a rectangular sheet after cutting squares from each corner, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the dimensions of the rectangular sheet**:
The dimensions of the rectangular sheet are given as 48 cm (length) and 27 cm (breadth).

2. **Determine the size of the squares cut from each corner**:
Each square cut from the corners has a side length of 3.5 cm.

3. **Calculate the new dimensions of the box after cutting the squares**:
- **Length of the box**:
The original length is 48 cm. Since we cut off 3.5 cm from both ends, we subtract 3.5 cm twice (once from each end):
\[ \text{New Length} = 48 - 2 \times 3.5 = 48 - 7 = 41 \text{ cm} \]

- **Breadth of the box**:
The original breadth is 27 cm. Similarly, we subtract 3.5 cm twice:
\[ \text{New Breadth} = 27 - 2 \times 3.5 = 27 - 7 = 20 \text{ cm} \]

4. **Determine the height of the box**:
The height of the box is equal to the side length of the squares cut off, which is 3.5 cm.

5. **Calculate the volume of the box**:
The volume \( V \) of a rectangular box is calculated using the formula:
\[ V = \text{Length} \times \text{Breadth} \times \text{Height} \]
Substituting the values we found:
\[ V = 41 \text{ cm} \times 20 \text{ cm} \times 3.5 \text{ cm} \]

6. **Perform the multiplication**:
- First, calculate \( 41 \times 20 = 820 \).
- Then, multiply by the height: \( 820 \times 3.5 = 2870 \text{ cm}^3 \).

### Final Answer:
The volume of the box is **2870 cm³**.