The circumference of the Earth, and the original metal band, is given by
C = 2 * pi * R
where R is the radius of the Earth in feet.
We splice in k inches of metal band. Thus, the circumference of the metal band is now
C + k = 2 * pi * r feet,
where r is the radius in feet of the metal band when shaped into a circle.
To find how much it is off the surface of the Earth, we first need to solve for r,
r = (C + k) / (2 * pi) = C / (2 * pi) + k/(2 * pi) = R + k / (2 * pi) feet.
To calculate how much off the circular metal band of radius r is off the Earth's surface of radius R, we subtract r from R,
R - r = k / (2 * pi) feet.
Letting k = 1 foot, we see that
R - r = 1 / (2 * pi) feet,
which is about 2 inches.