some more, just in case:
# parted -l (better than fdisk, I think)
# pvdisplay
# vgdisplay
# lvdisplay
In your case sdb does indeed seem to be unused!
Not memorized, but as much as I can remember off the top off my head, now all you need is:
pvcreate, vgextend, lvresize -r (resize FS)...