Campbell's Soup

 

To begin, let's solve the problem given! I did some research to determine that a soup can is about 11.6cm tall and 8.7cm in diameter. I also determined that the bicycle in the image (assuming that it was sized for an adult) was approximately 1.73m long. Obviously, there are a number of estimates being made here, but it looks as though the can is about three bicycles long, putting its 'height' at 5.18m. If we apply the ratio of the standard Campbell's soup can dimensions, we find that its radius should be 1.94m. We can then use the formula for volume of a cylinder (although there are some dents we can't account for) to determine that the volume of the water tank is approximately 61200000 cubic centimeters, or 61.2 kilolitres. 

My research suggested that an extremely large house fire would require 20000 gallons of water to control, or 76 kilolitres. The water tank, then, wouldn't quite be able to handle a massive house fire, but considering that Hornby Island is not full of sprawling mansions, it should be able to deal with a regular-sized house fire.

The extension that I would propose for this problem is to ask students why cans are sized the way that they are. A classic optimization problem (one that can be solved with graphing only) is to determine the optimal dimensions of a can to minimize surface area. Students can be directed to determine the optimal dimensions to hold the same volume as a Campbell's soup can and then, when they discover that the can is not optimal, ask furthering questions about why that might be. Surely someone at Campbell's has done this calculation! Why not use optimal dimensions?