I looked up some facts about the ark of the bible. The size was about 437-512 feet long and it was 3 stories high. If the average animal were the size of a sheep it could hold over 125,000 sheep. If the ark were rectangular there would have been over 100,000 sqare feet of floor space.
God instructed him to bring in mated pairs of every kind of bird,animal, reptile and every kind of creature that moves on the ground. He was even more specifically instructed to bring in 7 mated pairs of clean animals. Only air breathing animals needed to be included on the ark. Authorities on taxonomy estimate that there are less than 18,000 species of mammals, birds,reptiles and amphibians living in the world today. We might double this to allow for extinct species. This would give us 36,000 species times 2, or 72,000 animals. Allowing for the clean animals we might say there as many as 75,000 animals. Earlier we said there was enough for 125,000 sheep but most animals are smaller than the common house cat. There appears to be plenty of space of the preservation of animal life. However some creationist believe there were far fewer animals if Noah only took pairs of "kinds" as the word is used in Genesis 1. God created these "kinds" with potential for rich genetic diversity. For example at the time of Christ,there only existed two types of dogs. All the diversity that we see in the breeds of dogs came from these two!