jmc

If the diameter of the small circle is 2, then the radius is 1. Thus, the radius of the large circle is 4 times this, or 4. The area of the large circle is then $\pi 4^2=16\pi$ and the area of the small circle is $\pi 1^2=1\pi$. We can then find the gray area to be the difference in these, or $16\pi -1\pi =\boxed{15\pi }\text{sq units}$.