A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.

Answer

To find the area of the road that the road roller covers after 750 complete revolutions, we can follow these steps:

### Step 1: Find the radius of the road roller
Given the diameter of the road roller is 84 cm, we can find the radius by dividing the diameter by 2.

\[ \text{Radius} (r) = \frac{\text{Diameter}}{2} = \frac{84 \text{ cm}}{2} = 42 \text{ cm} \]

### Step 2: Convert the radius to meters
Since the length of the road roller is given in meters, we should convert the radius from centimeters to meters.

\[ r = 42 \text{ cm} = \frac{42}{100} \text{ m} = 0.42 \text{ m} \]

### Step 3: Identify the height of the cylinder
The height (length) of the road roller is given as 1 meter.

\[ h = 1 \text{ m} \]

### Step 4: Calculate the lateral surface area of the road roller
The lateral surface area (A) of a cylinder can be calculated using the formula:

\[ A = 2 \pi r h \]

Substituting the values of \(r\) and \(h\):

\[ A = 2 \times \frac{22}{7} \times 0.42 \times 1 \]

### Step 5: Calculate the area covered in one revolution
Calculating the above expression:

\[ A = 2 \times \frac{22}{7} \times 0.42 \times 1 = \frac{88 \times 0.42}{7} = \frac{36.96}{7} \approx 5.28 \text{ m}^2 \]

### Step 6: Calculate the total area covered after 750 revolutions
Now, we multiply the area covered in one revolution by the number of revolutions (750):

\[ \text{Total Area} = 750 \times 5.28 \approx 3960 \text{ m}^2 \]

### Final Answer
The area of the road that the road roller covers after 750 revolutions is approximately:

\[ \text{Total Area} \approx 3960 \text{ m}^2 \]

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