Soup Can Puzzle

This puzzle reminds me of Fermi problems, which my biophysics professor in my undergraduate studies taught me. More than a mere order-of-magnitude approach to solving problems, he taught us a beautiful new way to think about science.

To begin this puzzle, I purchased a can of Campbell's tomato soup. 

I made the following measurements with a ruler:

• Can radius: 2.3 cm
• Can height: 10cm
  

Next, I approximated the bike's height as equivalent to the radius of the water tank. Without the bike as a reference, we cannot approximate the radius of the water tank because there would be nothing to scale it to. I consider the bike's height to be 1 m. This tells us:

• Water tank radius: 1 m
  

Since the water tank has the same proportions to the soup can, we can find the height of the tank with one unknown in two equivalent ratios where three out of the four values are known. 

• Water tank height: 100/23 m
  

Next, the volume of the water tank is given by the volume of a cylinder:

• Volume of tank: ~ 14,000 L
  

Lastly, if we consider the average bungalow home to be 1500 square feet and that 1 gallon is required for every 3 square feet of fire, we would require 500 gallons, which is 1890 L.  

Note: Unit conversions are required from the imperial to the metric system because homes and fire data are commonly represented in square footage. 

 

In summary, when I consider a Campbell's soup can with radius 2.3 cm and height 10 cm and the bike as the radius (with height of 1 m) of the water tank, I find about 14,000 L in the tank, which is enough to put out about 7 house fires of 1500 square foot bungalows at a rate of 1 gallon per 3 square feet.