"How could all the animals fit on the Ark?"

Evidence Bible excerpt. (By Ken Ham, and Tim Lovett, answers in Genesis)

In the book Noah's Ark: a feasibility study, creationist researcher John Woodmorappe suggests that at most 16,000 animals were all that were needed to preserve the created kinds that God brought into the Ark. The Ark did not need to carry every kind of animal. . .nor did God command it. It carried only air-breathing, land-dwelling animals, creeping things, and winged animals such as birds (Gen. 7:14,15). Aquatic life (fish, whales, etc.), insects, and many amphibious creatures could have survived in suffient numbers outside the Ark. This cuts down significantly on the total number of animals that needed to be on board.

Another factor that greatly reduces the space requirements is this: the tremendous variety in species we see today did not exist in the days of Noah. Only the parent "kinds" of these species were required to be on board in order to repopulate the earth. For example, only two dogs were needed to give rise to all the dogs species that exist today. There are now than 200 species of dogs, from the miniature poodle to the St. Bernard various wolf species---all of which have descended from one original dog "kind." All other types of animals--cat kind, horse kind, Cow kind, etc.---have similarly been naturally and selectively bred to achieve the wonderful variation in species that we have today. God "programmed" this variety into the genetic code of all animal kinds--and even human kind! God also made it impossible for basic "kinds" of animals to breed and reproduce with each other. For example, cats and dogs cannot breed to make a new type of creature. This is by God's design, and it is one fact that makes evolution impossible.

Also, Noah wouldn't have taken the largest animals on the Ark, as there would be no reason to take "animal senior citizens" for a breeding population when the flood was over. It is more likely that he took younger juveniles aboard the Ark, which would have required less space and less food.

Using a short cubit of 18 inches to be conservative, Woodmorappe's conclusion is that "less than half of the cumulative area of the Ark's three decks need to have been occupied by the animals and their enclosures." This meant there was plenty of room for fresh food, water, and people. See Isa. 27:1 comment.

From Ray comforts  commentaryThe  Evidence Bible.