Assuming a diameter of 40mm and assuming hexagonal closest packed, 625 balls would fit in a cubic foot.
Boeing's website lists passenger volume for 747-400 as 31,285 plus cargo. 5536+835 = 37656 cubic feet
An estimate would be the number of balls in a cubic foot times volume = 23.5 million balls.
The volume of the fuel tanks would also need to be taken into consideration, as well as any other "empty" spaces. Maximum fuel capacity is 53,985 U.S. gal or 204,349 L. This adds another 7216.516 cubic feet. That's an additional 4,510,322 balls, which total 28 million ping pong balls.
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Approximately 19 million.
747 Classic 59.6 meters 747-400 64.4 meters 747-8 68.5 meters
747 = 1E7
747 - 414 = 333
0.5 x 747 = 373.5