Garry Conn

How many pennies would fit in a 4 ft deep 20 ft by 40 ft swimming pool?

By Garry Conn - Thu, Jan 17 2013, 11:00am CST

Each morning for about a week I have been wondering what the answer is to this question. And so now, I am going to solve it. I don't think it will be too difficult to figure out. Basically I want to know how many pennies would a swimming pool hold that is 4 feet deep, 20 feet wide and 40 feet long. If you know the best way to solve this problem let me know. The reason why I want to solve this problem is because I want to eventually write a PHP script that will automatically calculate and solve math problems such as this one. Contact me If you have some ideas about coding a script for this.

The first step in solving this problem is figuring out the size of a penny. I did a search and Yahoo Answers has the information here. I also verified these measurements here, which states the thickness as being 1.55 mm.

The thickness is needed in order to solve the problem, but the diameter isn't quite what I need. I basically need to know how long a penny is. This page mentions that a penny is .75 inches across.

So for the time being, I am going to assume both of these are true - a U.S. Penny is:

At this point, I need to figure out the volume of a penny. All the pennies would be lying flat on the pool, so I believe it would be best to calcuate the volume as if the penny were a box based on being .75 inches by .75 inches by .05 inches. Using this calculator, the results:

Using the same calculator, the volume of a swimming pool that is 4 feet deep, 20 feet wide and 40 feet long is:

Dividing the cubic gallons of the swimming pool by the cubic gallons of the penny equal 196,616,016 and dividing the cubic inches of the swimming pool by the cubic inches of the penny equal 196,608,000. I am not sure which answer is right, or if either is correct. My guess is the second answer because it is based on size rather than the measurement of a liquid. The pennies are all laying flat. However, if the math question involved melted pennies (liquid) then perhaps calculating the cubic gallon would be the way to go. If that were the case, then I would also use the diameter of the penny instead.

Which Answer is Correct?