A radio station broadcasts a signal over an area with radius of 50 miles. The station can relay the signal and broadcast over an area with a radius of 75 miles. How much greater is the area of broadcast region when the signal is relayed? Round your answer to nearest square mile.

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A = pi * r^2

A = 3.14 * 50^2
A = 7,850 square miles (area of the 50 mile broadcast signal)

A = pi * r^2
A = 3.14 * 75^2
A = 17,662.5 = 17,663 square miles (area of the 75 mile relayed signal)

Now we just need to subtract the 50 mile signal from the 75 mile signal, so:

17,663 - 7,850 = 9,813 square miles greater

Hope this helps :)

A = pi * r^2

A = 3.14 * 50^2
A = 7,850 square miles

Use the same method to find the area with a radius of 75 miles.

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To find how much greater the area of the broadcast region is when the signal is relayed, we need to calculate the difference between the areas of the two regions.

First, let's calculate the area of the original broadcast region with a radius of 50 miles. The formula to calculate the area of a circle is A = πr^2, where "A" is the area and "r" is the radius. So for the original broadcast region:

A1 = π(50)^2

Next, let's calculate the area of the broadcast region when the signal is relayed, with a radius of 75 miles:

A2 = π(75)^2

Now, to find the difference in the areas:

Difference = A2 - A1

Difference = π(75)^2 - π(50)^2

Difference = π(5625) - π(2500)

To round the answer to the nearest square mile, you can calculate the value of the difference and round it to the nearest whole number.

Please note that the value of π is approximately 3.1415, but for the purpose of this calculation, we'll keep it as π.

Let me calculate the difference for you.