My Solution on the Campbell Soup Problem

I began reading the problem as a student bird, Then I immediately started to list out the steps of solving this problem and then categorize them into 'Needs Research' (NR) or 'Needs Logic' (NL) for each.

Proposed Procedure to Solve the Problem

Step 1. (NR) Find out the shape and dimension of a typical Campbell soup can

Step 2. (NR & NL) Find out the length and height of a bicycle

Step 3. (NL) Calculate the dimension of the Campbell soup water tank. This can be achieved by either using the ratio between the soup can lid radius and soup can height and apply onto measurements of the water tank with respect to the bike

Step 4. (NL) Calculate the volume based on the estimated dimensions of the water tank from previous steps.

Step 5. (NR) Find out the average volume of water needed to put out a house fire

Step 6. (NL) Use a comparison between the estimated water tank volume from Step 4 and the average volume of water to put out a house fire from Step 5 to determine if it's enough.

Execution Result

Step 1. (NR) The soup can is a cylinder, hence only the radius/diameter of the lid/bottom and its height are needed. Andy Reynold has graciously offered his measurement of an actual can through the WhatsApp group. I can reasonably trust this source.  4.25 inches (10.80 cm) in height and 2.6 inches (6.60 cm) in diameter.

Step 2. (NR & NL) After contemplation, I am going to use the length of the bike (front wheel to back wheel) as the proportional reference to compare against the water tank. I found the average length to be 175cm through this website.

Step 3. (NL) I retrieved the pixel coordinates of the tips of the front and rear wheels of the bike (575 and 1190) and that of the water tank (555 and 2080). The pixel count (as a substitute for length) of the bike length is 615 pixels and that of the water tank height is 1525 pixels. Through the ratio of 2.4796748, I conclude the height of the water tank is 433.94 cm.

Step 4. (NL) If we assume the water tank and the soup can have the same proportion, then the height of the water tank is 433.94 cm and the diameter of the lid is 265.19 cm. The volume formula of the cylinder is the lid area * height which results in 23,968,113.50 cm^3 which can be converted to 23.968 m^3 (cubic meter) which is the volume of water it contains

Step 5. (NR) Through this website, I found that for an average one-story house of 1800 sqft, 600 gallons of water should suffice. Through conversion, 600 gallons of water is 2.27125 m^3.

Step 6. (NL) To compare the volume of the water tank (23.968 m^3) versus the volume of water needed to put out an average one-storey house (2.27125 m^3), I can conclude that the water tank holds more than enough water to put out multiple house fires regardless of the size.

As a teacher bird, I noticed how intricate this problem is for an educator. The following math tools are used when solving this problem.

1. Measuring a real-life object using a ruler or other tools (like on a computer screen)
2. Learning and using the appropriate unit of measurement
3. Navigate an ocean of conversion between imperial to metric and lower to higher degree
4. Double and triple checking your result through common sense
5. Reasonable estimation through comparison between objects

To extend this type of problem, I would ask the students to outline all the assumptions and estimations used in the calculation. The purpose is for students to defend and justify their choices of assumptions instead of blindly using them. Moreover, I would update the problem by encouraging students to find similar examples in their area of interest (sports, technology, astronomy) and ask them to provide estimation based on an image.