See the excerpt below for one view on this. The link will take you to the source. Christian evidences is a fascinitng study, but I also try to follow the cliche "God said it, I believe it, that settles it!"
The Ark measured 300x50x30 cubits (Genesis 6:15) which is about 140x23x13.5 metres or 459x75x44 feet, so its volume was 43,500 m3 (cubic metres) or 1.54 million cubic feet. To put this in perspective, this is the equivalent volume of 522 standard American railroad stock cars, each of which can hold 240 sheep. If the animals were kept in cages with an average size of 50x50x30 centimetres (20x20x12 inches), that is 75,000 cm3 (cubic centimetres) or 4800 cubic inches, the 16,000 animals would only occupy 1200 m3 (42,000 cubic feet) or 14.4 stock cars. Even if a million insect species had to be on board, it would not be a problem, because they require little space. If each pair was kept in cages of 10 cm (four inches) per side, or 1000 cm3, all the insect species would occupy a total volume of only 1000 m3, or another 12 cars. This would leave room for five trains of 99 cars each for food, Noah’s family and ‘range’ for the animals. However, insects are not included in the meaning of behemah or remes in Genesis 6:19-20, so Noah probably would not have taken them on board as passengers anyway. Tabulating the total volume is fair enough, since this shows that there would be plenty of room on the Ark for the animals with plenty left over for food, range etc. It would be possible to stack cages, with food on top or nearby (to minimize the amount of food carrying the humans had to do), to fill up more of the Ark space, while still allowing plenty of room for gaps for air circulation. We are discussing an emergency situation, not necessarily luxury accommodation. Although there is plenty of room for exercise, skeptics have overstated animals’ needs for exercise anyway. Even if we don’t allow stacking one cage on top of another to save floor space, there would be no problem. Woodmorappe shows from standard recommended floor space requirements for animals that all of them together would have needed less than half the available floor space of the Ark’s three decks. This arrangement allows for the maximum amount of food and water storage on top of the cages close to the animals.