Answer
$11\pi$
Work Step by Step
Step 1. We can identify the first equation as a circle centered at $(2,-3)$, with a radius $r_1=5$
Step 2. We can identify the second equation as a circle centered at $(2,-3)$, with a radius $r_2=6$
Step 3. The area of the donut-shaped region can be found as $\Delta A=\pi r_2^2-\pi r_1^2=\pi (6^2-5^2)=11\pi$
