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

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 :)