Puzzle for January 6, 2009

Yesterday, I decided to start saving pennies.
[remember: Each day I'll save double the number of pennies as the day before (ie today is one, tomorrow is two,
the next day will be four, etc). ]

How much room will I need for all these pennies?

How much room does a dollar in pennies take?

How about one thousand dollars? (assuming I keep it in penny form)

Is my 1400 square foot house big enough for one million dollars in pennies?

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The solution

The diameter of the penny can be easily obtained by using a ruler. I measured it as .75 inches or 19 Millimeters.

Now determining the thickness is going to be a challenge. Instead of trying to measure 1 penny's thickness why not several stacked together? (A roll of 50 pennies is 71.5 millimeters, making each penny 1.43 mm thick). Now we can get a rough idea of its volume. The penny is a cylinder with an extremely low height. As with all cylinders, the formula is:

VOLUME = Pi * (Radius)2 * height

VOLUME = 3.14159 * 9.5 * 9.5 * 1.27 = 360 cubic millimeters = .360 cubic centimeters. (per penny)

or non-metric: Volume = 3.14159 * .75 * .75 * .05 = .088 cubic inches

A million dollars of pennies would take a volume (not counting the spaces) of 100,000,000 * .088 cubic inches = 8,800,000 cubic inches (divided by 12 * 12 * 12 to convert to cubic feet) = 5092.59 cubic feet.

My 1400 square foot house has 8 foot ceilings

Volume of a rectangular shape = length * width * height or = base * height

My house's volume = 1400 square feet * 8 feet = 11,200 cubic feet

If there was nothing in my house, the pennies would fill about half of my house.

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