The geometry of popcorn

Meg recently bought old school popcorn, the kind you cook in a pot with oil. The instructions say to pour in enough popcorn to cover the bottom of the pot with a layer that is one kernel thick. This turns out to the be perfect number of kernels to fill the pot with popcorn. There must be some mathematical relationship between the area of a circle (the bottom of the pot)(PI * radius squared) and volume of a cylinder (a pot) (PI * radius squared * height) and expanding volume of popcorn.

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