Question

An FM radio station signal travels in a 40-mile radius. An AM radio station

Answer 1

Answer:

4976.28 square miles (nearest hundredth)

Step-by-step 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:

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