I know this is an old question, but since the article is up again... If you've seen the 5 gallon containers (with handles and lids) at Home Depot etc. (I have some that aquarium salt came in), that gives you a general reference. 5 gallon containers with sloped rather than straight sides (like those buckets) are probably 16-18" across, depending on the shape of the container. When in doubt, go bigger... but if all you have is a smaller container (or you've run short on potting mix), give it a shot anyway. One pepper plant will do fine in a 12-14" pot (I've even put 3 in a window box with only 6 or 7 inches of potting mix and added basil or something in between).
I'm dubious about planting a "roundup" of root veggies in a 12" deep container, unless you planted only a few seeds of each or thinned to give each veggie enough space to mature (going by spacing on the seed packet). However, you could plant lots of root veggies in a kiddie pool with a cracked bottom (or a new one with holes drilled in it). I'm tempted to try this, because root crops seldom do well in my garden soil... with a little thought, you could plant in concentric circles, varying the texture or color of the tops and trying to put something tallish in the center.
