Find the volume of the largest cylinder formed when a rectangular piece of paper 44 cm by 33 cm is rolled along its longer side.

Answer

To find the volume of the largest cylinder formed when a rectangular piece of paper measuring 44 cm by 33 cm is rolled along its longer side, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Dimensions of the Paper**:
- Length = 44 cm
- Breadth = 33 cm
- Since the paper is rolled along its longer side (44 cm), this will become the circumference of the cylinder.

2. **Set Up the Circumference Equation**:
- The circumference \( C \) of a cylinder is given by the formula:
\[ C = 2\pi r \]
- Here, \( C = 44 \) cm.

3. **Solve for the Radius \( r \)**:
- Substitute the circumference into the equation:
\[ 2\pi r = 44 \]
- Rearranging gives:
\[ r = \frac{44}{2\pi} \]
- Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{44}{2 \times \frac{22}{7}} = \frac{44 \times 7}{44} = 7 \text{ cm} \]

4. **Determine the Height of the Cylinder**:
- The height \( h \) of the cylinder is equal to the breadth of the paper, which is:
\[ h = 33 \text{ cm} \]

5. **Calculate the Volume of the Cylinder**:
- The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
- Substitute the values of \( r \) and \( h \):
\[ V = \pi (7^2)(33) \]
- Calculate \( 7^2 = 49 \):
\[ V = \pi \times 49 \times 33 \]
- Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{22}{7} \times 49 \times 33 \]
- Simplifying:
\[ V = 22 \times 7 \times 33 \]
- Calculate \( 7 \times 33 = 231 \):
\[ V = 22 \times 231 \]
- Finally, calculate \( 22 \times 231 \):
\[ V = 5082 \text{ cm}^3 \]

### Final Answer:
The volume of the largest cylinder formed is **5082 cm³**.