There is Power shell command by which you can get the details of Site collection listed in a content db.
List of Site collection from Content DB Name
PS C:\Users\Administrator > Get-SPsite -ContentDatabase WSS_Content
Result of this command will be like
Url
---
http://<Server Name>
http://<ServerName>/sites/SearchCenter
List of content DB from Site URL
PS C:\Users\Administrator > Get-SPContentDataBase -WebApplication http://<Server Name>
Result of this command will be like
Id : 6535eccc-0189-43d4-b022-5123e4ee8507
Name : WSS_Content
WebApplication : SPWebApplication Name=SharePoint - 80
Server : ServerName
CurrentSiteCount : 2