"Closed Activites"

I have a customer account that has over 90,000 records of "Closed Activities" they all need to be removed/deleted, (Don't ask how, I am the guy just fixing the issue!) my question or seeking conformation is, if I just delete this "Customer account" would this remove all 90,000 Closed Activity records? Then simply re-add his account information. I do not see anyway to "Bulk" delete them