the wheel of a vehicle has a diameter of 60 cm. how many times the wheel should rotate for the vehicle to travel a distance of 200 meters?

To determine how many times the wheel should rotate for the vehicle to travel 200 meters, we can follow these steps:

1. **Find the circumference of the wheel:** The circumference \( C \) of a circle is given by
   \[
   C = \pi \times d
   \]
   where \( d \) is the diameter.

   Given the diameter of the wheel is 60 cm, the circumference \( C \) is:
   \[
   C = \pi \times 60 \approx 188.4 \, \text{cm}
   \]

2. **Convert the total distance to the same units:** Since the circumference is in centimeters, convert 200 meters to centimeters:
   \[
   200 \, \text{m} = 200 \times 100 = 20000 \, \text{cm}
   \]

3. **Calculate the number of rotations:** To find the number of rotations \( N \), divide the total distance by the circumference of the wheel:
   \[
   N = \frac{\text{Total Distance}}{\text{Circumference}} = \frac{20000}{188.4} \approx 106.17
   \]

Since the wheel needs to complete full rotations, it would require approximately **106 full rotations** for the vehicle to travel 200 meters.

Would you like further details on any part of the solution?

Here are some related questions:
1. How would the answer change if the wheel diameter increased to 80 cm?
2. How can we calculate the distance traveled if we know the number of rotations?
3. How would this calculation work in miles or kilometers?
4. If the wheel made only 100 rotations, how far would the vehicle have traveled?
5. What is the formula for calculating wheel rotations for any given distance and diameter?

**Tip:** Remember to always use consistent units when working with measurements to avoid conversion errors.

The wheel of a vehicle has a diameter of 60 cm. How many times should the wheel rotate for the vehicle to travel a distance of 200 meters?

Learn how to determine the number of rotations needed for a vehicle wheel with a 60 cm diameter to travel 200 meters. This problem involves calculating the circumference and converting measurements, providing a clear solution for students in Grades 6-8.

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