can you plant carrots in a container if so how big does the container have to be?
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!