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It looks as if you can fit 9 cheese balls across the diameter, give or take, and if the jar is 6.5 inches across, then each piece is very roughly thee quarters of an inch in diameter. The jar isn't a perfect cylinder, but if it were, its volume would be ≈ 348 cubic inches. The balls aren't optimally packed, so any estimate is going to be not much better than a guess, but here goes: the volume of a sphere three quarters of an inch on a side is about a fifth of a cubic inch, so if we were optimally packing cubes that size into a larger rectangular prism with the same volume, we could fit about (348 * 5) = 1740 pieces. But we're 1) loosely packing 2) spheres into 3) an irregular cylinder with a 4) sloped top, and all four of these things take up space, so I'm going to guess that we can fit about half of that maximum, or about 850 cheese balls, into the jar.
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We can do a quick and dirty check on this number. If we calculate that there are about 9 cheese balls across the inner diameter of the jar, then we could fit about 70-75 balls per layer, depending on those indentations in the sides of the jar. (i can't prove this mathematically but I drew a diagram and that's what I came up with.) It looks like there are about 11 full layers (inasmuch as there are discrete layers at all) plus some more at the top, maybe a half a layer: (70 * 11.5) ≈ 805 cheese balls, (75 * 11.5) ≈ 863, averaging 834 total. That's within throwing distance of our estimate of 850.