A Miracle saved the world since Noah's Ark was too small to fit all the Animals

[edu]

If you start to calculate how much space, representatives of all the various creatures that do not live in the water take you will find, it is larger than all the space of the ark.
If so it was really a miracle that saved the animals of the world.
Why then did G-d want Noah to build the ark?
Answer 1 to make publicity to the world that a flood was coming in order to warn the people to change their ways, in order to nulllify the evil decree.
Answer 2 Even when G-d does miracles he likes to hide it as much as possible, and allows a person who doesn't reallly think deeply about things to ascribe the miracle to natural forces.

[muman613]

The reason, according to what I have heard is:

Hashem wanted Noach to actually build the ark. It took him 300 years to build it. The people of Noachs generation saw him building it and they should have been interested in what he was doing. This gave Noach time to try to bring the people to Teshuva. Of course in the end nobody did any Teshuva and Hashem brought the flood.

http://www.askmoses.com/en/article/416,2163225/Noah-and-the-Flood-Apocalypse.html

Again, without waiting for the affirmative response he didn't want to hear, Rabbi Steinsaltz continued. Noah was in that situation. His compatriots had benefited from generation after generation of warnings to mend their ways. They had turned a deaf ear to the righteous Methusaleh, who had pleaded with them. Decades before, a merciful G-d had asked Noah to publicly build a large ark, a project that would take him over a hundred years, in order to draw attention to His plans, and afford people another chance to repent.

None of this had done any good. Noah was mocked and derided by all, without exception. A lesser person would have doubted his sanity, or at least given up trying to swim against such a powerful current.