jmc

Let the sphere have radius $r$. A sphere with radius $r$ has surface area $4\pi r^2$, so we have $$4\pi r^2=196\pi .$$ Dividing both sides by $4\pi$ yields $r^2=49$; taking the square root of both sides and keeping the positive solution yields $r=7$ inches.

A great circle of a sphere is the circular cross-section of the sphere that passes through the sphere's center, which, in this case, is a circle with radius 7. The circumference of this circle is $2\pi \cdot 7=\boxed{14\pi }$ inches.