A rectangular sheet of paper ` 44 cm xx 18 cm ` is rolled along its length and a cycllinder is formed. Find the radius and the volume of the cyclinder formed.

Answer

To solve the problem of finding the radius and volume of the cylinder formed by rolling a rectangular sheet of paper measuring 44 cm by 18 cm along its length, we can follow these steps:

### Step 1: Understand the dimensions of the cylinder
When the rectangular sheet is rolled along its length (44 cm), the length of the sheet becomes the circumference of the base of the cylinder, and the breadth (18 cm) becomes the height of the cylinder.

- Circumference (C) = 44 cm
- Height (h) = 18 cm

### Step 2: Use the formula for the circumference of a circle
The circumference of a circle is given by the formula:
\[ C = 2\pi r \]
Where \( r \) is the radius of the cylinder.

### Step 3: Substitute the known value into the formula
Substituting the circumference into the formula, we have:
\[ 2\pi r = 44 \]

### Step 4: Solve for the radius \( r \)
To find \( r \), we can rearrange the equation:
\[ r = \frac{44}{2\pi} \]

Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{44}{2 \times \frac{22}{7}} \]
\[ r = \frac{44 \times 7}{44} \]
\[ r = 7 \text{ cm} \]

### Step 5: Calculate the volume of the cylinder
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]

### Step 6: Substitute the values into the volume formula
Using \( r = 7 \) cm and \( h = 18 \) cm:
\[ V = \pi (7^2)(18) \]
\[ V = \pi (49)(18) \]

Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{22}{7} \times 49 \times 18 \]

### Step 7: Simplify the volume calculation
First, simplify \( \frac{22 \times 49 \times 18}{7} \):
\[ V = \frac{22 \times 49 \times 18}{7} = 22 \times 49 \times \frac{18}{7} \]
\[ V = 22 \times 49 \times 2.57 \] (approximately)
Calculating \( 49 \times 18 = 882 \):
\[ V = \frac{22 \times 882}{7} \]
\[ V = 22 \times 126 = 2772 \text{ cm}^3 \]

### Final Answers
- Radius \( r = 7 \) cm
- Volume \( V = 2772 \) cm³