Question

p-1. semi-trailer trucks have an odometer on one hub of a trailer wheel. the hub is weighted so that it does not rotate, but it contains gears to count the number of wheel revolutions—it then calculates the distance traveled. if the wheel has a 1.15 m diameter and goes through 200,000 rotations, how many kilometers should the odometer read?

Explanation:

Calculate the circumference of the wheel

$$ C = \pi \cdot d = \pi \cdot 1.15\text{ m} \approx 3.61283\text{ m} $$

Calculate the total distance in meters

$$ D_{\text{meters}} = 200,000 \cdot C = 200,000 \cdot (1.15\pi)\text{ m} = 230,000\pi\text{ m} \approx 722,566.31\text{ m} $$

Convert the distance to kilometers

$$ D_{\text{km}} = \frac{230,000\pi}{1000}\text{ km} = 230\pi\text{ km} \approx 722.57\text{ km} $$

Answer:

\(723\text{ km}\) (or approximately \(722.57\text{ km}\))