Question

HOw far away can a person live from a radio station and hear its broadcast if the signal covers a circular area of 40000 square miles?

Answer 1

The radio station is at the center of a circle with an area of 40,000 square miles. The furthest point that you could hear the broadcast would be on the outer edge of the circle or at the end of the radius of the circle. The formula for the area of a circle is:

Area = π
`r^(2)`

So we take what we know and work the formula in reverse.

40,000 = πr²

40,000 / π = r²

12,732.4 = r²

√12,732.4 = √r²

112.84 = r

The radius of a circle with an area of 40,000 square miles is 112.84 miles. This is the furthest point that you would be able to hear the broad cast.

Explanation: