You may find the better answers in the maths section.

Actually, I would say ZERO millimeters. The question states that GOLD is only on the outer edge. Then, is asks to find the surface area of the gold, EXCLUDING the edge of the coin.

Since the gold is only on the edge, and we are excluding the edge, the answer is zero.

Surface area covered with gold

= Area of the inner circle – Area of the outer Circle

= πR^2 – πr^2

= π (R^2 – r^2)

The image

http://s122.photobucket.com/albums/o275/theedifier/?action=view¤t=doubloon-1.jpg

AB is the length of the tangent drawn touching the inner circle

= 33 mm

Draw OC perpendicular to AB

Thereby, OC bisects AB

==> AD = DB = 11.5 mm

In the right angled triangle ODB

OB = r (Radius of the inner circle)

OD = R (Radius of the outer circle)

DB = 11.5 mm

By pythagerous theorem

OB^2 = OD^2 + DB^2

==> r^2 = R^2 – (11.5)^2

==> (11.5)^2 = R^2 – r^2

Thus, the Surface area covered with gold

= π (R^2 – r^2)

= π (11.5)^2

If it is double sided required area = 2 * π (11.5)^2

http://www.theedifier.com/