Answer
$11\pi$
Work Step by Step
Given the circles $$(x-2)^2+(y+3)^2=25$$ $$(x-2)^2+(y+3)^2=36$$ we notice that both circles are centered at $(2,-3)$, and their radii are $r_{1}=\sqrt{25}=5$, $r_{2}=\sqrt{36}=6$
The area of a circle is given by the formula $\pi r^2$.
The area of circle $1$ is, $\pi r_{1}^2=25\pi$ and the area of circle $2$ is, $\pi r_{2}^2=36\pi$.
The area between the two circles is the area of the donut-shaped region: $$36\pi-25\pi==11\pi.$$
