A rectangular sheet of paper 44 cm x 18 cm is rolled along its length and a cylinder is formed. The volume of the cylinder so formed is equal to (Take `pi`= 22/7)

Options

A. 2772 `cm^(3)`
B. 2506 `cm^(3)`
C. 2460 `cm^(3)`
D. 2672 `cm^(3)`

Answer

To solve the problem, we need to find the volume of the cylinder formed by rolling a rectangular sheet of paper with dimensions 44 cm (length) and 18 cm (breadth).

### Step-by-Step Solution:

1. **Identify the dimensions of the cylinder**:
- When the rectangular sheet is rolled along its length, the length of the sheet becomes the circumference of the base of the cylinder.
- Therefore, the circumference \( C \) of the cylinder is equal to the length of the sheet:
\[ C = 44 \, \text{cm} \]
- The height \( h \) of the cylinder is equal to the breadth of the sheet:
\[ h = 18 \, \text{cm} \]

2. **Relate circumference to radius**:
- The formula for the circumference of a circle is given by:
\[ C = 2\pi r \]
- Setting the circumference equal to 44 cm, we have:
\[ 2\pi r = 44 \]

3. **Solve for the radius \( r \)**:
- Rearranging the equation to find \( r \):
\[ r = \frac{44}{2\pi} \]
- Substituting \( \pi = \frac{22}{7} \):
\[ r = \frac{44}{2 \times \frac{22}{7}} = \frac{44 \times 7}{44} = 7 \, \text{cm} \]

4. **Calculate the volume of the cylinder**:
- The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
- Substituting the values of \( \pi \), \( r \), and \( h \):
\[ V = \frac{22}{7} \times (7)^2 \times 18 \]
- Simplifying this:
\[ V = \frac{22}{7} \times 49 \times 18 \]
- The \( 7 \) in the denominator cancels with one of the \( 7 \)s in \( 49 \):
\[ V = 22 \times 7 \times 18 \]

5. **Calculate the final volume**:
- Now, calculating \( 22 \times 7 \times 18 \):
\[ V = 154 \times 18 = 2772 \, \text{cm}^3 \]

### Final Answer:
The volume of the cylinder formed is \( 2772 \, \text{cm}^3 \).

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