Editor's note: Before you read the posting below, check this page on 'The origin of the whole nine yards'.
I, too, had heard that this saying derived from the amount of material in a truck -- but, I'd heard dump truck rather than cement truck. No matter. The reason I'm writing is that I can tell you the phrase certainly pre-dates the 1970's. I remember it vividly from when I was a kid back in the 1950's and I wouldn't be surprised if it didn't come into usage before that.