Can anyone tell me how to increase the space available to the root space to say 500 gigs??
(https://xfxtech.com/Image1.jpg)
check the mount point.
Probably it is in different disk or block storage
try this command to see disk info:
df -h
you might search Google for more commands and how to mount a disk
since this is a LVM you would need to check for available space with pvscan but you probably don't have any available space so you would need to decrease /home and then increase root partition, note that you can increase space online but to decrease home you would need umount it.
with a decrease, if you don't know what you are doing you can get all your data lost so do a backup of home before