Well, when you have a shape inside of a shape, the area of the region outside of the inner shape is almost always:
So, we know that:
We also know that the area of a circle is:
And we get:
Basically, say you have a paper circle of radius R, and you cut out a smaller circle of radius R - 3, you are left with the shaded region you described. It therefore makes sense that all you do is take the area of the larger circle and subtract, or take away, the area of the smaller circle to get the desired area.
Hopefully this helps.