רמב"ן — עשה לך תיבה

Q — Why such precise dimensions for the teiva? Even ten arks couldn't hold every species and a year's food — so the gathering itself required a miracle ('החזיק מועט את המרובה'). If the miracle was inevitable, why not build it small?

A — Two answers. (1) Hashem wanted it large so that the people of the dor would see it, wonder at it, ask about it, and 'אולי יעשו תשובה' — the ark was an extended invitation to repent. (2) The foundational hashkafic principle: 'כן הדרך בכל הניסים שבתורה או בנביאים לעשות מה שביד אדם לעשות, והשאר יהיה בידי שמים' — when Hashem performs a nes, He minimizes its scope, requiring human השתדלות for everything within human power. Build the ark as large as possible; the miracle picks up only what man cannot.