Final answer:
By calculating the circumference of the wheel with a diameter of 1.15 meters and multiplying it by the number of rotations (200,000), we find that the total distance traveled is 722.4 kilometers. Hence, the odometer should read approximately 230 kilometers, option C.
Step-by-step explanation:
To determine how many kilometers the odometer should read after 200,000 rotations of a trailer wheel with a diameter of 1.15 meters, we first need to calculate the circumference of the wheel, which is the distance the truck travels with one rotation of the wheel.
The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter of the circle. Using the given diameter of 1.15 meters:
C = π(1.15 meters)
C = 3.612 meters (rounded to three decimal places)
Now, to find the total distance traveled, we multiply the circumference by the number of rotations:
Total distance = Circumference × Number of rotations
Total distance = 3.612 meters/rotation × 200,000 rotations
Total distance = 722,400 meters
Since the question asks for the distance in kilometers, we need to convert meters to kilometers:
Total distance = 722,400 meters ÷ 1,000 meters/kilometer
Total distance = 722.4 kilometers
Therefore, the correct option for the distance the odometer should read after 200,000 wheel rotations is C. 230 kilometers, as this is the rounded value to the nearest ten kilometers.