radius of 1.3 miles. If the mayor wants a new siren that can cover double the area

Question

A severe weather siren in a local city can be heard within a radius of 1.3 miles. If the mayor of the city wants a new siren that can cover double the area of the old siren, what should the radius of the new siren be?

Answer 1

The area of the siren's original coverage is:

 

A = π(1.3)² = 1.69π mi².

 

The mayor wishes to double the coverage area, so you need to solve the equation

 

2(1.69π) = πr² for the radius r.

 

Here:

 

3.38π = πr²

r² = 3.38

r = √3.38 ≈ 1.84 mi.