Question

how many miles of land area does a tower with a signal of 15 miles in all directions cover

Answer 1

The area of a circle with a radius of 15 is about 707 or exactly 706.86

Answer 2

Such a tower covers a circle with center in the tower and radius 15 miles.

The area of a circle is $\pi r^2$, so in your case it is

$A=\pi r^2 = \pi 15^2=225\pi$

If you need to approximate this number, recall that $\pi=3.1415\ldots$