Formula to Calculate the Number of Revolutions

Oct 13, 2025 by miodeya.com 24 views

**A Road Roller Has Length 2m and Radius 140cm: Find the Number of Revolutions Required by the Roller to Cover an Area of 616m²**

A road roller is a crucial piece of equipment used in construction and road maintenance to flatten and smooth out surfaces. It is essentially a cylindrical object with a length and a radius. In this article, we will explore the concept of a road roller and how to calculate the number of revolutions required to cover a given area.

To solve this problem, we need to understand the relationship between the area covered by the road roller and the number of revolutions it makes. The area covered by the road roller is given as 616m², and we need to find the number of revolutions required to cover this area.

Given Values

Length of the road roller (l) = 2m
Radius of the road roller (r) = 140cm = 1.4m
Area to be covered (A) = 616m²

Formula to Calculate the Number of Revolutions

The formula to calculate the number of revolutions required to cover a given area is:

Number of Revolutions (N) = (π × r × A) / (l × π × r²)

where π is a mathematical constant approximately equal to 3.14.

Simplifying the Formula

We can simplify the formula by canceling out the π and r terms:

N = A / (l × r)

Plugging in the Values

Now, we can plug in the given values into the simplified formula:

N = 616 / (2 × 1.4) N = 616 / 2.8 N = 220

Therefore, the number of revolutions required by the road roller to cover an area of 616m² is 220.

Q: What is the formula to calculate the number of revolutions required to cover a given area? A: The formula to calculate the number of revolutions required to cover a given area is: N = (π × r × A) / (l × π × r²)

Q: Can we simplify the formula? A: Yes, we can simplify the formula by canceling out the π and r terms: N = A / (l × r)

Q: What is the value of π used in the formula? A: The value of π used in the formula is approximately 3.14.

Q: How do we plug in the values into the simplified formula? A: We plug in the given values into the simplified formula: N = A / (l × r)

Q: What is the final answer to the problem? A: The final answer to the problem is 220.

Q: What is the relationship between the area covered by the road roller and the number of revolutions it makes? A: The area covered by the road roller is directly proportional to the number of revolutions it makes.

Q: How do we calculate the number of revolutions required to cover a given area? A: We use the formula: N = (π × r × A) / (l × π × r²) to calculate the number of revolutions required to cover a given area.

Q: What is the significance of the radius of the road roller in the formula? A: The radius of the road roller is used in the formula to calculate the number of revolutions required to cover a given area.

Q: Can we use the simplified formula to calculate the number of revolutions required to cover a given area? A: Yes, we can use the simplified formula: N = A / (l × r) to calculate the number of revolutions required to cover a given area.

Q: What is the final answer to the problem? A: The final answer to the problem is 220.