Azzure

There are carrots very suitable to grow in containers - short or round like Thumbelina, Parmex, Little finger, to name just few. Check this thread: What Edibles for Railing Containers?, same question asked.

I think that container should be min. 10" deep.

For 'regular' carrots you need deeper container.

Phooto below is not mine, found on net:

I was thinking of doing it in a storage container like a 30 gallon one

Short varieties less than 8 inches I think. Regular size about 12-14 inches high. Easy to do in containers and SO YUMMY!