a tires circumference in 31 inches, how many rotations will the tire make in 10,000 miles, show all calculations
To find the number of rotations the tire will make in 10,000 miles, we need to calculate the distance traveled per rotation.
Circumference of the tire = π * diameter
Since we are given the circumference as 31 inches, we can find the diameter by dividing it by π:
Diameter = 31 inches / π ≈ 9.87 inches
Now, we need to calculate the distance the tire will travel in one rotation:
Distance traveled per rotation = circumference of the tire = π * diameter ≈ 3.14 * 9.87 inches ≈ 31.01 inches
To convert this distance to miles, we need to divide by 12 (since there are 12 inches in a foot) and then divide by 5280 (since there are 5280 feet in a mile):
Distance traveled per rotation in miles ≈ 31.01 inches / 12 / 5280 ≈ 0.00049375 miles
Now, to find the number of rotations in 10,000 miles, we divide the total distance traveled by the distance traveled per rotation:
Number of rotations = 10,000 miles / 0.00049375 miles per rotation ≈ 20,246,753.97 rotations
Therefore, the tire will make approximately 20,246,753.97 rotations in 10,000 miles.