Chapter 11.6, Problem 22WE

To determine

To Find: The approximate ratio of area of shaded region to the unshaded region.

Answer to Problem 22WE

  $1.983$

Explanation of Solution

Given:

  

  

Here

  $\begin{array}{l}{A}_1=A_3\\ A=lb\\ A=(60)(325)\\ A=19500\end{array}$

Now

Area of sector of section second.

  $\begin{array}{l}{A}_2=\frac{90}{360}\pi r^2\\ $ A_2=\frac{1}{4}\pi {(60)}^2$A_2=900\pi \end{array}$

Area of sector of section fourth.

  $\begin{array}{l}{A}_4=\frac{90}{360}\pi r^2\\ $ A_4=\frac{1}{4}\pi {(325)}^2$A_4=\frac{105625}{4}\pi \end{array}$

Now

Ratio of shaded region to unshaded region is

  $\begin{array}{l}R=\frac{A_4}{A_1+A_2+A_3}\\ R=\frac{\frac{105625}{4}\pi }{19500+19500+900\pi }\\ R=1.983\end{array}$

Hence, $1.983$