A reactangular sheet of dimension `33cmxx18cm` is rolled along its breadth to form a cylinder. Find the radius of the cylinder.

Answer

To find the radius of the cylinder formed by rolling a rectangular sheet of dimensions 33 cm x 18 cm along its breadth, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Dimensions**:
The dimensions of the rectangular sheet are given as:
- Length (L) = 33 cm
- Breadth (B) = 18 cm

2. **Identify the Rolling Direction**:
The sheet is rolled along its breadth (18 cm). When the sheet is rolled, the breadth becomes the circumference of the base of the cylinder formed.

3. **Use the Formula for Circumference**:
The circumference (C) of a cylinder is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius of the cylinder.

4. **Set the Circumference Equal to the Breadth**:
Since the breadth of the sheet becomes the circumference of the cylinder:
\[ 2\pi r = 18 \text{ cm} \]

5. **Solve for the Radius (r)**:
Rearranging the equation to find \( r \):
\[ r = \frac{18}{2\pi} \]
Simplifying this gives:
\[ r = \frac{18}{2 \times 3.14} = \frac{18}{6.28} \approx 2.86 \text{ cm} \]

6. **Final Answer**:
Therefore, the radius of the cylinder is approximately:
\[ r \approx 2.86 \text{ cm} \]