A rectangular paper of width 14 cm is rolled along its length and a cylinder of radius 20 cm is formed. Find the volume of the cylinder. `("Take" pi = (22)/(7) )`

Answer

To find the volume of the cylinder formed by rolling a rectangular paper of width 14 cm along its length, we can follow these steps:

### Step 1: Identify the dimensions of the cylinder
- The radius \( r \) of the cylinder is given as 20 cm.
- The height \( h \) of the cylinder is equal to the width of the rectangular paper, which is 14 cm.

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

### Step 3: Substitute the values into the formula
We know:
- \( \pi = \frac{22}{7} \)
- \( r = 20 \) cm
- \( h = 14 \) cm

Substituting these values into the formula:
\[ V = \frac{22}{7} \times (20)^2 \times 14 \]

### Step 4: Calculate \( r^2 \)
Calculate \( r^2 \):
\[ r^2 = 20 \times 20 = 400 \]

### Step 5: Substitute \( r^2 \) back into the volume formula
Now substitute \( r^2 \) back into the volume formula:
\[ V = \frac{22}{7} \times 400 \times 14 \]

### Step 6: Calculate \( 400 \times 14 \)
Calculate \( 400 \times 14 \):
\[ 400 \times 14 = 5600 \]

### Step 7: Substitute and simplify
Now substitute this back into the volume formula:
\[ V = \frac{22}{7} \times 5600 \]

### Step 8: Calculate the volume
To calculate \( \frac{22 \times 5600}{7} \):
\[ 22 \times 5600 = 123200 \]
Now divide by 7:
\[ V = \frac{123200}{7} = 17600 \, \text{cm}^3 \]

### Final Answer
The volume of the cylinder is:
\[ \boxed{17600 \, \text{cm}^3} \]