An automobile tire is rated to last for 35,000 miles. To an order of magnitude, through how many revolutions will it turn?

To determine the number of revolutions an automobile tire will make over a distance of 35,000 miles, we need to know the circumference of the tire.

The formula for the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius of the circle.

However, we only have the distance the tire will travel, not the circumference or radius. We can use the distance traveled and the circumference to find the number of revolutions.

To calculate the number of revolutions, we can use the formula: Revolutions = Distance / Circumference.

Assuming that the tire is a perfect circle when it touches the ground, we can estimate the circumference of the tire by using the formula C = πd, where d represents the diameter of the tire.

To an order of magnitude, we can approximate π to be 3. Therefore, C = 3d.

Given that we have the distance (35,000 miles), and we need to find the number of revolutions, we need to determine the circumference. To do that, we need the diameter.

To estimate the diameter, we can use the average wheel size for an automobile, which is around 28 inches. However, this can vary depending on the specific vehicle.

Now, let's calculate the diameter:
Diameter = Average Wheel Size / 12 (to convert inches to feet)

Diameter = 28 / 12 = 2.33 feet

Next, we can calculate the circumference using the formula C = 3d:
Circumference = 3 * 2.33 = 6.99 feet

Finally, we can calculate the number of revolutions using the formula:
Revolutions = Distance / Circumference.

Revolutions = 35,000 miles * 5280 feet/mile / 6.99 feet

Revolutions ≈ 27,919 revolutions.

Therefore, to an order of magnitude, an automobile tire rated to last for 35,000 miles would turn approximately 27,919 revolutions.