Do you have a case or a screen protector on the iPhone? Try removing them to ensure they are not blocking the the ear speaker. Also, that volume can only be adjusted when in a phone call. When in the call, put the phone up to your ear and try increasing the volume with the side buttons and see if that helps.
The Related Article above your name in your post also provides other troubleshooting steps, and if they fail to correct the problem, they recommend that you contact Apple Support. You can use the link at the top of the page, or if you have an Apple Store close by, make a Genius Bar appointment to allow Apple to examine the device. They will explain your options.