Chosen Solution

I purchased a new Samsung Momentus 4TB hard drive for my iMac (EMC 2638). The old 1TB drive functioned OK, I just needed more space. I hooked the new drive up with an external USB cable and formatted it. Next I took the new drive out of the iMac and then used a duplicator and made a sector by sector duplicate of the old drive to the new one. I then installed the new drive and reassembled unit. On boot I used Cmd/Opt/P/R to reset the VRAM. Then I checked disk utility and it shows up exactly the same as the old drive. How do I claim my new space?

Click on the drive in disk util (not the partition) and hit partition. You should be able to resize it to 4tb.