Archeology has also found evidence of larger cubits, sometimes called royal cubits, ranging from 21 to 25 inches. If the ark was measured in one of these larger cubits, it could have been more than 600 feet long and 100 feet wide. The ark had 3 decks, with subcompartments on each deck for different animals. That means there was between 150,000 and 190,000 square feet of floor space with fairly high ceilings. And with some stacking of cages for smaller creatures, they could be just fine.
Many animals hibernate, further reducing the space and food required to support the animals.
You are to bring into the ark two of all living creatures, male and female, to keep them alive with you. Two of every kind of bird, of every kind of animal and of every kind of creature that moves along the ground will come to you to be kept alive. You are to take every kind of food that is to be eaten and store it away as food for you and for them. Noah did everything just as God commanded him. Most of us would be so focused on the physical details of the story as to miss the important spiritual aspect.