It might be a good idea to verify that pages in those folders do actually return a 410 response. If it does you do need to wait for G to crawl them. The only way they offer to remove content requires that you do not block those pages or folders in robots.txt.
Look in your Google Webmasters Tools account to get instructions from Google on how to remove pages, folders and directories from their index. If the pages exist you need to make sure they don't have metatags of "index, follow" and do not block them in robots.txt or they can't crawl to see that the pages have noindex tags. When you have fixed the metatags, then notify Google via GWT to remove that content from their index. It does not always work with one try, they still bug me about directories that were properly removed years ago and do not exist anywhere except their imagination.
Edited to add: Make sure that pages you want to disappear are not showing up in your sitemaps.