AMC 12A 2006 Problem 12

A number of linked rings, each 1 \mathrm{~cm} thick, are hanging on a peg. The top ring has an outside diameter of 20 \mathrm{~cm}. The outside diameter of each of the other rings is 1 \mathrm{~cm} less than that of the ring above it. The bottom ring has an outside diameter of 3 \mathrm{~cm}. What is the distance, in \mathrm{cm}, from the top of the top ring to the bottom of the bottom ring?

Answer Choices
A. 171
B. 173
C. 182
D. 188
E. 210