Answer
r$\approx$3979 miles
circumference $\approx 25,000$ miles
Work Step by Step
He assumes that the sun rays are parallel,
so by alternate angles of a transversal,
the central angle is also $\theta=7.2^{o}$.
To convert into radians, multiply by $\pi/180^{o}$.
The length $s$ of an arc that subtends
a central angle of $\theta$ radians is $ s=r\theta$.
Solving for r,
$ r=\displaystyle \frac{s}{\theta}=\frac{500}{7.2^{o}\cdot\frac{\pi}{180^{o}}}\approx$3978.8735773
r$\approx$3979 miles
The circumference is
$ 2\pi r=2\pi\cdot 3979\approx$25000.7943373
$\approx 25,000$ miles
