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The ark according to the NIV was 450 feet long by 75 feet wide by 45 feet high having three decks of 15 feet. The square feet area of a deck, 33,750 sq ft. is smaller than a modern football field with the field dimensons being 120 by 360, 43,200sq ft. Now on this ark was not only all the animals of the earth in pair but also Noah and family and provisions to last the more than 250 days until the door is opened. Now the total deck surface of the ark is 33,750 x 3 equals 101,250 square feet. And the total volume is 101,250 times 15 or 1,518,750 cubic feet (56,250 cubic yards). Is it possible to store all the animals and provisions for the time period in this space?

Yes, but you have a few misconceptions. It wasn't two of every animal. It was animal "kinds". A kind might be thought of as a species. For example a wolf might be a canine "kind". These "kinds" then diversified into the forms we have today. Also some animals could survive without being on the ark...amphibians, many types of insects, etc etc could survive a flood.

There's many other suppositions that you've got wrong but this is just for starters...

Also some animals could survive without being on the ark...amphibians, many types of insects, etc etc could survive a flood.

Creationist theories about creation of the fossil record during the flood posit floodwater conditions that would kill anything in the water.