Trigonometry · Superchallenge problem

A bicycle's odometer assumes the wheel's rolling radius is always exactly $30$ cm, and so reports a distance of $2\pi\cdot30$ cm for every wheel rotation. Over the course of a $10000$-rotation ride the tire actually wears down evenly, so its TRUE rolling radius decreases from exactly $30$ cm at the first rotation to exactly $29$ cm at the ten-thousandth, shrinking by the same tiny amount on each successive rotation. Modelling each rotation as a circle at its own true radius, find by how many cm the odometer's reported distance OVERSTATES the bicycle's true distance travelled.