The Zip-loc challenge is pretty old, but I was doing it today to test my knowledge of chemistry. The way I calculated the volume of a ziplock bag was to fill to with water and find the calculate how much water was put in.
My Question:
Is there a purely mathematical way to calculate the volume of said ziplock bag? Two thoughts came to mind:
1) Use a Fourier series to represent the bag in a 2D coordinate system, and use axes of rotation to come up with an answer
2) Use a multivariable function to model the bag, and use a double integral to calculate volume
Would either of these methods be viable? And if they are, does it make sense to solve for an exact value rather than use the approximation when filling with water?
P.S: I'm nit really sure what SE this would belong on, but I thought since my question was mostly mathematical, this would be the right one.
Thanks in Advance!
EDIT:
For those wondering, the dimensions of the particular bag I was using is 16.5 x 14.9 cm