Pennies average about 3 grams.
Pennies are about 0.4 cubic centimeters, or 0.4 ML.
There are 100,000,000 pennies in a million dollars.
So...we're talking 300,000 kg.
We're talking 40,000,000 cubic centimeters, or 40 cubic meters.
The volume isn't so atrocious; maybe completely fill a couple of spare bedrooms or an entire basement. I mean, don't get me wrong it would be annoying. But the weight...would destroy most houses. That's about 100x the weight most houses are designed to support.
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Cats land on their feet. Toast lands peanut butter side down. A cat with toast strapped to its back will hover above the ground in a state of quantum indecision