One volume button does not work

If the physical button doesn’t work, it will require repair.

It is a common misconception that an iPad (or iPhone) can remain fully functional with damaged or defective physical buttons. 

Whilst Accessibility features (such as assistive touch) can be used to augment the User Interface, these features cannot be used as a substitute for physical button sequences that must be used to trigger system recovery actions. Sooner or later, as now, you will encounter a situation from which you cannot recover.

Until repaired, you will not be able to resolve a locked-out (disabled) iPad - or reset a forgotten device passcode.

iPad Repair & Service - Apple Support

For qualifying devices, in lieu of repairing your own iPad, Apple usually offer an exchange for a renewed/reconditioned device of the same model and specification. The cost of the exchange is exactly the same as the flat-rate repair. The exchange device is your to keep - and will have a limited warranty.

I doubt that the Genius Bar does board-level repairs. They will instead do an exchange as they stated. If you want a board-level repair, try a third-party repair shop. Going this route however, Apple likely will not touch the device if it needs any additional repair/service.

Just go to the nearest repair shop. Probably it's broken.