Chapter 15, Problem 42CR

To determine

To find: the difference of the area of the shaded region above and below $\overline{XY}$ .

Answer to Problem 42CR

  $121\pi$ .

Explanation of Solution

Given:

The circles $O,P,Q,\text{and}R$ are tangent as shown in the given figure.

  

The radius of $\odot R=11$

Calculation:

According to the question, the difference of the area of the shaded region above and below $\overline{XY}$ will be the area of $\odot R$ .

Then,

  $\begin{array}{l}A\odot R=\pi r^2\\ =\pi {\left(11\right)}^2\\ =121\pi \end{array}$

Thus, the difference of the area of the shaded region above and below $\overline{XY}$ is $121\pi$ .