I have my db kept at /mnt, using ephemeral storage that comes with ec2 instance. To take the backup using ec2 api tools we need a volume id, but in the aws console I can find the volume id of only the 8gb root storage.
What should I do if want the backup of ephemeral storage? Is there any alternative for backing up instance storage?
First and foremost, you should never store anything of lasting value on ephemeral storage in Amazon EC2, except if you know exactly what you are doing and are prepared to always have point in time backups etc. - your question seems to indicate that you might be mistaken about the concept of ephemeral storage, the respective difference between Amazon EC2 Instance Storage an Amazon EBS and the significant implications regarding data safety and backup requirements:
Ephemeral storage will be lost on stop/start cycles and can generally go away, so you definitely don't want to put anything of lasting value there, i.e. only put temporary data there you can afford to lose or rebuild easily, like a swap file or strictly temporary data in use during computations. Of course you might store huge indexes there for example, but must be prepared to rebuild these after the storage has been cleared for whatever reason (instance reboot, hardware failure, ...).
These explanations should clarify why you are unable to backup the ephemeral storage volumes with a mechanism that solely applies to EBS volumes (i.e. EBS snapshots). Accordingly, you can backup the former via regular operating system level backup tool of your choice, with Duplicity being a popular choice optionally facilitating Amazon S3 for example, as addressed in my answer to Easiest to use backup software for live linux server.