Extend LVM

First, unmount the LVM in question.

Then, extend it:

lvextend -L+10G /dev/virtualdisk/vol

Boot into Virtualhost

Unmount the drive, rerun partition reader, remove the partition and resize it; then remount.

partprobe
fdisk /dev/hdd

Remove partition, create as new larger partition,

Resize it:

resize2fs /dev/hdd1