jmc

The area of a circle with radius $r$ is $\pi r^2.$

So the area of the larger circle is $\pi (10^2)=100\pi$ and the area of the smaller circle is $\pi (6^2)=36\pi .$

The area of the ring between the two circles is the difference of these two areas.

Therefore, the area of the ring is $100\pi -36\pi =\boxed{64\pi }.$