Detect unmounted volumes on selected disk with PowerShell WMI or Diskpart

Question

How do I link unmounted volumes to physical disks?

Say I need to find and mount unmounted volumes on disk 3 as numbered by Diskpart or WMIC, or PowerShell WMI. How do I find out, with a script, what volumes of disk 3 aren't mounted? Or, alternatively, what physical disk a given unmounted volume (having no DriveLetter) resides on?

When a volume is unmounted, no logical disk or mount point exist for it. I suppose the relation can be found with GetRelated method, but I can't find such a code example suited for the task.