Chapter 1, Problem 22PT

To determine

To find the radius of the new siren

Answer to Problem 22PT

1.8 miles

Explanation of Solution

Given information:

Radius of old siren = 1.3 miles

Formula used:

To calculate radius of siren use $\pi r^2$

Calculation: substitute value of old radius in the formula

  $\pi {(1.3)}^2$

According to the question mayor wants new siren that will cover double area

New area= $2\times \pi {(1.3)}^2$

Let R be the radius of new siren

Therefore, area of siren= New area

Substituting values in the formula

  $\pi R^2=2\times \pi {(1.3)}^2$

Solving it further

  $R^2=2{(1.3)}^2$

Solving it further

  $R=\sqrt{2{(1.3)}^2}$

Solving it further

  $R=\sqrt{2(1.69)}$

Solving it further

  $R=\sqrt{3.38}$

Calculating value of underroot

  $R=1.8$ Miles