how many grains of sand in a beach volleyball court?

Have you ever thought about how many stars there are in the sky or how many grains of sand on the beach?

If you know how to figure out volumes you can estimate how many grains of sand there are in a beach volleyball court that Colleen plays in. It isn't too hard so here is how we do it.

You need to know how big a grain of sand is. It turns out sand comes in all sizes, but the beach sand in Southern California is small. It is also very beautiful when you look at it under a microscope. This photo is of beach sand from a beach near where Colleen plays.

The thing about sand is that it comes in all kinds of shapes and there is a lot of air between them even when you scrunch it down. We'll make a good guess. We won't be able to figure out exactly how many grains of sand there are in the volleyball court, but we will get a good idea.

The black bar in the photo is one millimeter long. We're going to use the metric system because it is easier to do the arithmetic. A millimeter is small - there are a bit more over 25 of them in an inch. Colleen is two meters tall and a millimeter is 1/1000 of a meter, so she is 2000 millimeters tall. How tall are you in millimeters?

We are going to try to get an idea of how many grains of sand will fit in a cube that is a millimeter on a side. One way to guess is to get the average number of grains on a millimeter long line. Remember that the volume of a cube is its hight times its width times its depth. These are all the same, so the number of grains of sand in a millimeter is multiplied times itself there times. It is "cubed" You will get slightly different numbers depending on where you measure, but 2 grains per millimeter is a pretty good average. 2 times 2 times 2 is 8, so we will say there are 8 grains of in a cube that is a millimeter on a side. Some sand is smaller and some is larger.

Now all we have to do is figure out how many of these cubes fit in a beach volleyball court and we are almost done. We need to know the length, width and depth of the sand. It is pretty bumpy, but we are just making an educated guess, so we will pretend the depth is even. It turns out the courts are 8 meters wide and 16 meters long. The sand can be deep, but lets say it is about a half meter deep (this is about 20 inches). So the volume is 8 * 16 * 1/2 cubic meters, or 64 cubic meters.

That is a lot of sand!

Lets convert this to millimeters. Each meter is 1000 millimeters, so a cubic meter has 1000 x 1000 x 1000 cubic millimeter - 1,000,000,000 ... a billion cubic millimeters. So our beach volleyball court has 64 billion cubic millimeters in it. Since there are 8 grains of sand in each cubic millimeter we just multiply

64,000,000,000 cubic millimeters * 8 grains of sand per cubic millimeter = 512,000,000,000 - grains of sand. That is more than half a trillion! There are about 6 million people on Earth so you could give each of them nearly 100 grains of sand from Colleen's court.

This is just an estimate, but if someone asks, you can tell them there are probably over 500 billion grains of sand in a beach volleyball court, but that depends on how big the sand is.

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