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Assuming this is one of those "offbeat" interview questions. My answer is what I honestly would say vocally without research or paper to write formulas.
If the approximate diameter of the plane is 20 feet, then I have a 10 foot radius, I can't remember the exact formula for area of a circle but if I made four squares of 10 feet and dived by 3 that would be a close guess. So 10 feet = 120 inches x 120 inches = 14,400 square inches x 3 = 43,000 square inches. So for every inch of volume I can fit 43,000 bearings. My best guess on the length of the plane is 200 feet, so 43,000/inch = ~500,000/foot. Therefore I would estimate that 100 million bearings could fit inside the skin of a completely empty 747.
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