Final answer:
To find the number of revolutions tires make while traveling 80,000 km, convert the distance to meters and calculate the tire's circumference; then divide the total distance by the tire's circumference. The tires make approximately 49,020,263 revolutions.
Step-by-step explanation:
The student's question involves finding out how many revolutions an automobile's tires make if the tires have a radius of 0.260 meters and travel a total distance of 80,000 kilometers. To perform the calculation, we start by converting the travel distance from kilometers to meters, since the radius of the tire is given in meters.
Since 1 kilometer is equivalent to 1,000 meters, we convert 80,000 kilometers into meters by multiplying it by 1,000:
80,000 km × 1,000 m/km = 80,000,000 meters
Next, we calculate the circumference of the tire, which is the distance a tire covers in one complete revolution:
Circumference = 2 × π × radius
Circumference = 2 × π × 0.260 m = × π × 0.260 m = × 3.14159 × 0.260 m ≈ 1.633 m
Finally, we divide the total distance traveled by the circumference of a tire to find the number of revolutions:
Number of revolutions = Total distance ÷ Circumference
Number of revolutions = 80,000,000 m ÷ 1.633 m ≈ 49,020,263 revolutions
Therefore, the tires make approximately 49,020,263 revolutions before wearing out, not accounting for any backing up or wear that might affect the radius.