Final answer:
To determine the number of tire revolutions, calculate the circumference with the formula (2πr) using the given tire radius, and then divide the total distance traveled by that circumference. For a tire with a radius of 0.260 m over 80,000 km, this results in approximately 48,982,071 revolutions.
Step-by-step explanation:
The question addresses a problem involving the calculation of the number of revolutions a tire makes over a certain distance. To find the number of revolutions, we can use the formula for the circumference of a circle (C = 2πr, where r is the radius) and divide the total distance traveled by the circumference of the tire.
The radius of the tire is provided as 0.260 meters, and the total distance traveled by the automobile is 80,000 kilometers (which needs to be converted to meters, as 80,000 kilometers is equal to 80,000,000 meters). Using the formula:
- Circumference of the tire (C) = 2π(0.260 m)
- Number of revolutions (N) = Total distance traveled / Circumference
Therefore:
- C = 2π(0.260 m) ≈ 1.633 m
- N = 80,000,000 m / 1.633 m
- N = 48,982,071 revolutions (approximately)
The automobile's tires make approximately 48,982,071 revolutions before wearing out.