How do I find my model number?

I am working on a friends 27inch iMac. When I looked at it in detail today, I found out that the hard drive is failing. Since the hard drive is going bad, the Apple menu is unaccessible and I cannot find the model number to purchase the appropriate hard drive. My friend told me that he thinks it is a 2010 model but he's not sure. I have tried looking up the numbers below the barcodes on the computer box, but I can't seem to find any information online (even from the Apple website). Can anyone tell me or help me find out the model number of this computer so I can purchase the appropriate hard drive and accessories or at least give me an idea on which hard drive to purchase? I want to be absolutely sure.

Here are the specs as printed on the box;

• 27 inch (viewable) 16:9 widescreen LED-backlit display; 2560 by 1440 pixels
• 3.2 GHz Intel Core i3 processor; 4MB shared level 3 cache
• 4GB of 1333 MHz DDR3 SDRAM; supports up to 16GB
• 1TB Serial ATA hard drive
• 8x slot-loading SuperDrive DVD+R DL/DVD+RW/CD-RW)
• ATI Radeon HD 5670 graphics processor with 512MB of GDDR3 memory
• Built in iSight video camera
• Built in 10/100/1000BASE-T Ethernet (external DSL and cable modem ready)
• SD card slot, FireWire 800 port, four high-speed USB 2.0 ports
• Built in AirPort Extreme wireless networking (802.11n)2 and Bluetooth 2.1 + EDR
• Audio: Built-in stereo speakers; integrated microphone; optical digital audio input/audio line in; optical digital audio output/headphone out
• Mini DisplayPort output port with support for VGA3, DVI4, and dual-link DVI5, also supports input from external DisplayPort sources
• Apple Wireless Keyboard and wireless Magic Mouse
• Preinstalled Mac OS X and iLife6
• Meets ENERGY STAR requirements

Barcode below specs displays number: 826-9111-A

Barcode inside box flap displays number: 602-7110-A

Any help is greatly appreciated. Thank you.