How much room does 1 billion pennies take up?

Answer 1

I did this exercise today because I was curious.
What_is_the_diameter_of_a_US_penny says that the diameter of a penny is 19.05 mm by 1.55 mm high.

For every four pennies stacked side by side in a line, 3 inches of space is taken up. You can then figure this out with simple math and trial and error. There is probably a more complicated formula that can be used, but this is how I did it:

4(n) by 4 (n) = 3 (n) by 3 (n) gives you the size of your square in terms of both pennies and inches

1,000,000,000 / 4(n) by 4 (n) = 3 (n) by 3 (n) gives you how many rows of pennies you would need to have to lay out 1,000,000,000 pennies, or y.

Multiply the number of rows by the height, or 1.55 mm * y and you know how tall your cube is, or z. The size of your cube is then is 3 (n) by 3 (n) by z.

To answer your question, 1,000,000,000 pennies, if you were to lay them out in a square of 800 by 800 pennies and build a cube by repeating this process, the cube would be 50'L x 50'W x 8'H. A good visual for this is to go stand in a two-car garage and imagine 4.5 of those full of pennies, or look at a single-story house floor plan for 2,500 square feet (usually about 3-4 bedrooms) and imagine filling it up with pennies (flat ceiling heights are commonly 8' in the US).

Cheers!