How many peas to fill a bath tub?

Estimate the quantity of regular green peas required to fill a standard bath tub to the 'brim' . One million? One hundred-thousand? How many ?





give or take a few tens of thousandsHow many peas to fill a bath tub?
The American Standard 2470 tub holds a volume of 227 liters.


Use the close packing of spheres constant to calculate the maximum amount of volume taken up by peas, then change this volume from liters to cubic meters.


V=227(pi/(3*sqrt(2))=168 liters=168 L*(0.001 m^3/L)=0.168 m^3


Assume each pea is 0.5 cm in diameter and approximately a sphere.


The radius is then 0.25 cm=0.0025 m and the volume of the pea is


V=(4*pi/3)r^3=6.5x10^(-8) m^3


The number of peas is then the volume of the tub divided by the volume of the pea,


N=0.168/6.5x10^(-8)=2,566,850 peasHow many peas to fill a bath tub?
One really large pea. Or three the size of beachballs.





Ok... regular peas. Think of the volume of a 10x10x10 cube of peas... I'd put that at about 3x3x3 or 27 cubic inches. Lets say 25 cubic inches to make things easier and to include settling. A cubic foot is 12^3 cubic inches... or about 7000 of our peas. I'd put a standard bathtub on the order of about 20 cubic feet (2x2x5=20) which puts us at 140000 peas. Given that I'm not off by a factor of 10, though I suppose I could be, I'd say one million is out of the question.
If the estimated size of a pea is 1 cm3, it might take 2700 probably...?
depends on how much you drank last night