An fm radio station signal travels in a 40 mile radius an am radio station signal travels in a 4 mile radius how much more area does the fm station cover than the am station?

You're talking about circular areas.

-- The area of a circle is (pi) x (radius)2 .

-- The area of the 4-mile radius is (pi) x (4)2 = 16 pi square miles

-- The area of a circle is proportional to the square of its radius.

So the area of the 40-mile radius is (10)2 = 100 times the area of

the 4-mile radius = 1,600 pi square miles.

The larger circle has (99 times the area of the 4-mile radius) more area

than the smaller circle has.

(99) x (16 pi) = 1,584 pi = 4,976.3 square miles more than the smaller circle.