Thursday, September 27, 2007

The Density of Jelly Beans

Last night my wife was telling me about a contest our daycare is running. They have a medium sized bottle sitting out on a desk filled with miniature multi-colored chocolate kisses. The ones that you use for baking. You are supposed to guess the number of kisses in the container. If you are closest you get some sort of prize.

So this morning I go in and take a look at the setup. It wasn't anything fancy, just a clear plastic cylindrical container filled with kisses. I start thinking of ways to approximate the answer. Here is my thinking:

1) Count the number of kisses along the circumference of the cylinder. Call this number C. In this instance it was 56.
2) Compute the cylinder's radius R by the formula C = 2 x pi x R. It comes out to about 8.9.
3) Count how many kisses high the cylinder is. Call this number H. I counted H to be about 10 kisses.
4) Plug this into the volume equation V = H x pi x R x R. So V is approx 2500 kisses.

This is the answer I submitted however the drawing isn't until tomorrow.

On my drive into work I started thinking of better ways to approximate the answer. It seems to me you could take a few random containers of known volume from around the house, fill them with chocolate kisses, and estimate the density of them. Then you could apply this density to any sized container to compute a more accurate answer.

Surely there must already be a site out there that lists density of various objects for these contests? Alas I could not find one. I did find this site on jelly bean density however. I think the jelly beans they use are the old fashioned, larger jelly beans as opposed to the smaller Jelly Belly type beans common today. But it still may be useful... one day... perhaps...

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