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If you divide the area of the US (9,826,630 km^2) by the surface area of a penny (285.02 mm^2), you get 3.4477 x 10^16 pennies, or about 34 quadrillion (million x billion).
However, if you actually did this on a flat space the size of the US, the densest arrangement would be a sort of staggered/honeycomb pattern. In this case, the effective space taken up by each penny is 314.28 mm^2, so you could only fit 31.27 quadrillion, or about $313 trillion.
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