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The problem states:

A road roller has a diameter of 0.7 m and a width of 1.2 m. We are tasked with finding the number of revolutions that the roller must take in order to level a playground of size 120 m by 44 m.

### Steps to Solve:

1. **Calculate the Circumference of the Roller:**
   The circumference \( C \) of a roller (cylinder) is given by the formula:
   \[
   C = \pi \times d
   \]
   where \( d \) is the diameter of the roller. Given \( d = 0.7 \, \text{m} \), we calculate the circumference.

2. **Calculate the Area Covered by One Revolution:**
   The area covered by one full revolution of the roller is the width of the roller multiplied by its circumference:
   \[
   A_{\text{roller}} = C \times \text{width}
   \]
   Given the width of the roller is 1.2 m, we can now compute the area covered per revolution.

3. **Calculate the Total Playground Area:**
   The area of the playground is:
   \[
   A_{\text{playground}} = 120 \, \text{m} \times 44 \, \text{m}
   \]

4. **Calculate the Number of Revolutions:**
   The total number of revolutions required is the total area of the playground divided by the area covered by one revolution:
   \[
   N = \frac{A_{\text{playground}}}{A_{\text{roller}}}
   \]

Let me now compute the required values.The road roller must take approximately **2001 revolutions** to level the entire playground of size 120 m by 44 m.

Would you like more details on any of the steps?

Here are 5 related questions for further exploration:
1. How would the number of revolutions change if the diameter of the roller were increased?
2. How does the width of the roller affect the total number of revolutions?
3. What if the playground area was not a rectangle—how would you calculate the required revolutions?
4. How can you generalize this approach to irregularly shaped playgrounds?
5. How do different types of rollers (e.g., conical rollers) affect surface area coverage?

**Tip:** Always double-check the units of measurements in problems involving geometry, as they can lead to errors in calculations if inconsistent.

A road roller has a diameter 0.7 m and its width is 1.2 m. Find the number of revolutions that the roller must take in order to level a playground of size 120 m by 44 m.

Learn how to find the number of revolutions a road roller must take to level a playground of size 120 m by 44 m. This problem involves calculating the circumference of a roller and using area formulas. Suitable for students in Grades 6-8.

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