Mathematics problems in primary schools need detailed problem-solving process.

The circumference formula of a circle: c = 2π r; The area formula of the circle: s = π r 2;

The radius of circle b: r= 15.7/2π=2.5 (cm).

Because the area of circle A is eight times that of circle B,

So the area of circle A is S=8*(2.5*2.5)*π= 157 (square centimeter).

R 2= 157/π=50 (cm), r≈7.07 (cm).

Then the diameter of the nail ring d = 2r = 2 * 7.07 =14.5438+04 (cm).

(note: I don't know if it's right, it's probably like this! If it is wrong, I'm sorry! )