Last night, I was fortunate to attend a presentation at the McConnell Arts Center in Worthington, Ohio by Zack Hample, ball hawk extrordinaire and author of 3 baseball books, including "The Baseball: Stunts, Scandals, and Secrets Beneath the Stitches", which I read and enjoyed immensely. He even autographed a baseball for me, here is the pictographic proof:
Zack signed my ball with the number 6309, which is his up to the minute count of his baseball collection. At first, I thought that this number of balls would take up multiple storage units, but then I did the math, because that is what I am good at.
A set of whole number factors that comes close to 6309 is 20 times 20 times 16, which is 6400. A standard Rawlings baseball box that stores one baseball is approximately 2 13/16" cubical, which means that if you stacked baseballs in their boxes in a layer of 20 by 20, making it 16 boxes high, the footprint of the stack on the floor would be 4'8" by 4'8", and the stack would be 3'9" tall.
The weight is another matter, however. At 5 ounces per, 6309 baseballs would weight about 1972 pounds. That is (almost) a ton of balls.