finding iMac's production date

Welcome to Apple Support Communities.

Please, do not install a hard drive yourself. We'll help you find a solution, but we must know the year.

On the bottom of the iMac's stand is a serial number. Enter it here: Check Your Service and Support Coverage - Apple Support, and let us know what it says.

Jack

Please check OWC for details of changing/upgrading hard drives in your Mac. Their Instructional videos are very detailed. They also sell drives and installation kits.

If it's a 2011, then here are OWC's videos for that model (check to make sure the model ID is correct):

https://eshop.macsales.com/installvideos/imac_27_mid_2011/

And no, you really don't want to do that yourself and professional installation will be quite expensive. Remember it's 10 years old; it is time to retire it.