The radius of a cylindrical roller is 140 cm and its length is 100 cm. It takes 500 complete revolutions to level a playground completely. Find the area of playground in `m^(2)`.

Answer

To solve the problem step by step, we will follow the outlined procedure to find the area of the playground leveled by the cylindrical roller.

### Step 1: Identify the given values
- Radius of the cylindrical roller (r) = 140 cm
- Length of the cylindrical roller (h) = 100 cm
- Number of revolutions = 500

### Step 2: Calculate the curved surface area (CSA) of the cylindrical roller
The formula for the curved surface area of a cylinder is:
\[ \text{CSA} = 2 \pi r h \]
Substituting the values:
\[ \text{CSA} = 2 \times \frac{22}{7} \times 140 \times 100 \]

### Step 3: Simplify the calculation
1. Calculate \(2 \times \frac{22}{7} = \frac{44}{7}\).
2. Now, multiply by the radius and height:
\[ \text{CSA} = \frac{44}{7} \times 140 \times 100 \]
3. First, calculate \(140 \times 100 = 14000\).
4. Now, calculate:
\[ \text{CSA} = \frac{44 \times 14000}{7} \]
5. Calculate \(44 \times 2000 = 88000\).
6. Finally, divide by 7:
\[ \text{CSA} = 88000 \text{ cm}^2 \]

### Step 4: Calculate the total area covered in 500 revolutions
The area covered in 500 revolutions is:
\[ \text{Total Area} = \text{CSA} \times \text{Number of Revolutions} \]
\[ \text{Total Area} = 88000 \times 500 \]
Calculating this gives:
\[ \text{Total Area} = 44000000 \text{ cm}^2 \]

### Step 5: Convert the area from square centimeters to square meters
To convert from square centimeters to square meters, we use the conversion factor:
\[ 1 \text{ m}^2 = 10000 \text{ cm}^2 \]
Thus, we convert:
\[ \text{Area in m}^2 = \frac{44000000 \text{ cm}^2}{10000} \]
Calculating this gives:
\[ \text{Area in m}^2 = 4400 \text{ m}^2 \]

### Final Answer
The area of the playground is:
\[ \boxed{4400 \text{ m}^2} \]