Was the ark large enough to hold all the required animals?
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, Noahs 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 dont 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 Arks three decks. This arrangement allows for the maximum amount of food and water storage on top of the cages close to the animals.
Food requirements
The Ark would probably have carried compressed and dried foodstuffs, and probably a lot of concentrated food. Perhaps Noah fed the cattle mainly on grain, plus some hay for fibre. Woodmorappe calculated that the volume of foodstuffs would have been only about 15 % of the Arks total volume. Drinking water would only have taken up 9.4 % of the volume. This volume would be reduced further if rainwater was collected and piped into troughs.
The above is an extract from answersingenesis.org
In terms of numbers and sizes The largest animals were probably represented by teenage or even younger specimens. The median size of all animals on the ark would actually have been that of a small rat, according to Woodmorappes up-to-date tabulations, while only about 11 % would have been much larger than a sheep.
Also you would not take 1 of each type of cow but rather 1 of each genus type. Woodmorappe's totals calculate about 8000 genera, including extinct genera, thus about 16,000 individual animals which had to be aboard.
