Answer
The circumference of the earth is 24,800 miles
Work Step by Step
We can convert the angle to radians:
$\theta = 7^{\circ}12'$
$\theta = (7+\frac{12}{60})^{\circ}$
$\theta = (7.2^{\circ})(\frac{\pi~rad}{180^{\circ}}) = 0.1257~rad$
We can find the earth's radius:
$S = \theta ~r$
$r = \frac{S}{\theta}$
$r = \frac{496~mi}{0.1257~rad}$
$r = 3945.9~mi$
We can find the circumference $C$ of the earth:
$C = 2\pi~r$
$C = (2\pi)(3945.9~mi)$
$C = 24,800~mi$
The circumference of the earth is 24,800 miles
