Question

A radio station broadcasts a signal over qn area with a 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 the broadcast region when the signal is relayed? Round your answer to tje nearest sqaure mile

Answer 1

The difference in the areas of the broadcast region when the signal is relayed is approximately 9812 square miles.

Step-by-step explanation:

To find the difference in the areas of the broadcast region when the signal is relayed, we can use the formula for the area of a circle, which is A = πr^2.

First, let's calculate the area of the broadcast region without relaying the signal. The radius is 50 miles, so the area is A = π(50)^2 = 2500π square miles.

Next, let's calculate the area of the broadcast region with the relayed signal. The radius is 75 miles, so the area is A = π(75)^2 = 5625π square miles.

The difference in the areas is 5625π - 2500π = 3125π square miles. To round this to the nearest square mile, we can use the approximation π ≈ 3.14. Therefore, the difference in the areas is approximately 3125 * 3.14 = 9812 square miles.

Answer 2

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 :)