How well does the radius of a tree correlate with its age?
The radius of tree is not a good measure of the tree age, the most efficient technique to know the age of a tree is with dendrochronological methods, this is the less invasive technique. However, knowing very well the dynamics of growth of each species you can infer the age, check out this study: 

Jan Lukaszkiewicz and Marek Kosmala. 2008. Determining the Age of Streetside Trees with Diameter at Breast Height-based Multifactorial Model (note this is a direct link to a pdf)