Thursday, 15 October 2015

Estimating the volume of a campbell soup water tank


First of all, I want to point out that pictures are deceiving.  Although it looks like the bottom of the bike wheel starts below the lowest point of the water tank, one can see on closer examination that part of the tank is buried in sand (understandably, to keep the tank from rolling away!)  Furthermore, since the top of the water tank is further away than the bike, we have to adjust our perspective slightly so as to take this into account.  Overall, I would estimate that the diameter of the water tank is 2.2 times the height of the bike.
To determine the height of Susan's bike, I measured the height of a medium-frame bike I have at home.  It was 102 cm.
The diameter of the water tank is therefore 102cm x 2.2 = 224cm.
According to an online source (https://sketchup-math.wikispaces.com/Campbell's+Soup), a Campbell soup can has a height of 4 inches and a radius of 1 and 5/16 inches.  Therefore it has a diameter of 2 and 5/8 inches.  Therefore, the height is 4/(2+5/8)=1.52 times the diameter.  Apply this now to the water tank.  The water tank's length (equivalent to a can's "height") will be 1.52x224cm=341cm.
The volume of the tank will therefore be pi*radius^2*height = pi*(224/2)^2*341 = 13450000 cm^3 = 13450000mL = 13 500L = 3550 gallons!

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