A rectangular paper of 22 cm `xx` 12 cm is folded in two different ways and formed two cylinders .
(i) Find the ratio of the volumes of two cylinders
(ii) Find the difference of the volumes of two cylinders.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine the dimensions of the two cylinders formed by folding the rectangular paper.

1. **Folding along the breadth (12 cm)**
- Height (h1) = 22 cm
- Circumference = 12 cm
- Using the formula for circumference: \( C = 2\pi r \)
- Therefore, \( 2\pi r = 12 \)
- Solving for radius (r1):
\[ r_1 = \frac{12}{2\pi} = \frac{6}{\pi} \]

2. **Folding along the length (22 cm)**
- Height (h2) = 12 cm
- Circumference = 22 cm
- Using the formula for circumference: \( C = 2\pi r \)
- Therefore, \( 2\pi r = 22 \)
- Solving for radius (r2):
\[ r_2 = \frac{22}{2\pi} = \frac{11}{\pi} \]

### Step 2: Calculate the volumes of both cylinders.

1. **Volume of the first cylinder (V1)**
- Using the formula for the volume of a cylinder: \( V = \pi r^2 h \)
- Substituting the values for the first cylinder:
\[ V_1 = \pi \left(\frac{6}{\pi}\right)^2 \cdot 22 \]
- Simplifying:
\[ V_1 = \pi \cdot \frac{36}{\pi^2} \cdot 22 = \frac{792}{\pi} \]

2. **Volume of the second cylinder (V2)**
- Substituting the values for the second cylinder:
\[ V_2 = \pi \left(\frac{11}{\pi}\right)^2 \cdot 12 \]
- Simplifying:
\[ V_2 = \pi \cdot \frac{121}{\pi^2} \cdot 12 = \frac{1452}{\pi} \]

### Step 3: Find the ratio of the volumes of the two cylinders.

- The ratio \( \frac{V_1}{V_2} \):
\[ \frac{V_1}{V_2} = \frac{\frac{792}{\pi}}{\frac{1452}{\pi}} = \frac{792}{1452} \]
- Simplifying the ratio:
\[ \frac{792 \div 36}{1452 \div 36} = \frac{22}{40.5} = \frac{11}{20.25} \approx \frac{11}{20} \]

### Step 4: Find the difference of the volumes of the two cylinders.

- The difference \( V_1 - V_2 \):
\[ V_1 - V_2 = \frac{792}{\pi} - \frac{1452}{\pi} = \frac{792 - 1452}{\pi} = \frac{-660}{\pi} \]
- Converting to a numerical value (using \( \pi \approx 3.14 \)):
\[ \frac{-660}{3.14} \approx -210.38 \text{ cm}^3 \]

### Final Answers:
1. **Ratio of the volumes**: \( \frac{11}{20} \)
2. **Difference of the volumes**: \( 210 \text{ cm}^3 \)