Question

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?

Answer 1

4976.28 square miles (nearest hundredth)

Explanation:

`\textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}`

FM radio station

Given:

• r = 40 miles

`\implies \textsf{Area}=\pi (40)^2=1600 \pi \: \sf miles^2`

AM radio station

Given:

• r = 4 miles

`\implies \textsf{Area}=\pi (4)^2=16 \pi \: \sf miles^2`

Difference:

`\begin{aligned}\implies \textsf{FM area - AM area} & =1600 \pi - 16 \pi\\ &= 1584 \pi\\ & =4976.23\:\textsf{square miles (nearest hundredth)}\end{aligned}`