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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?

Respuesta :

semsee45

Answer:

4976.28 square miles (nearest hundredth)

Step-by-step explanation:

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

FM radio station

Given:

  • r = 40 miles

[tex]\implies \textsf{Area}=\pi (40)^2=1600 \pi \: \sf miles^2[/tex]

AM radio station

Given:

  • r = 4 miles

[tex]\implies \textsf{Area}=\pi (4)^2=16 \pi \: \sf miles^2[/tex]

Difference:

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

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