Answer
The wheel would have made $2.1\times10^6$ revolutions.
Work Step by Step
We know that $s=r\theta$
Here $s$ is the distance of the race, so $s=4520km=4.52\times10^6m$ and $\theta$ is the number of revolutions the wheel makes during the race.
- In situation 1, we have $\theta_1=2.18\times10^6rev=1.37\times10^7rad$. We can find the wheel's radius: $$r=\frac{s}{\theta_1}=0.33m$$
- In situation 2, the wheel's radius is $r=0.33m+0.012m=0.342m$; we have $$\theta_2=\frac{s}{r}=1.32\times10^7rad=2.1\times10^6rev$$
