I finally found the source of the error and it was in the arrangement of the parentheses. I believe I'm using the arrangement you suggested. Below is the working code.
$solid_moment=$solid_weight*(pow($solid_diameter/2,2)/2);
$hollow_moment=$hollow_weight*((pow($hollow_od/2,2)+pow($hollow_id/2,2))/2);
I was surprised to find the problem in the parentheses. I'm not a great mathematician but I'm used to working with parentheses in Excel. Apparently I need to become a better mathematician.
Thanks again for your help and for checking back.