A Pi Day Puzzle

Yesterday was Pi Day. The day in which the month and day of the calendar is 3/14, the first three digits to the mathematical formula for pi.

Stamps of Distinction posted a puzzle that relates to pi.

Suppose you could put a steel band tightly around the equator of Earth. Assume, for the sake of this puzzle, that the earth is perfectly round, without hills or valleys, and that the steel band would make an exact circle around the Earth where it is touching the surface evenly. Then, you take a cutting torch, open up a gap in this band, and weld in exactly 1 extra meter (for non-metric readers, approximately 1 yard) of metal.

Question: how high would this extra meter of material allow the band to be raised, evenly, throughout the entire circumference of the earth. If you haven't heard this question before, the answer will likely amaze you.

(thanks Tony)