Tomato Soup Can

 

Q1. Lots of math problems could come out of this story. Here's one: given the size of the actual Campbell's Soup can (of normal size) and the height of the bike in the photo, what are the dimensions of the volunteer fire department's water tank? What is its volume? Does it hold enough water to put out an average house fire?

The average height of a bike is 31 inches (according to Google). The bike in the photo looks to be approximately one third of the height of the can. Of course, the can is on its side so 31x3=93 inches represents the diameter of the can. Therefore, the radius of the can is 46.5 inches, quite big. Radius is the most important variable when considering volume because it has the highest power so the fact that this water tank has a big radius means it probably can hold enough water to put out an average house fire.

According to Google, a house fire requires about 1 gallon of water for every 3 square feet of house. To be on the conservative side, which is where you want to be when it comes to emergency situations like house fires, lets say an average house on Honrby Island is 2000 square feet. This is an educated guess because this statistic is harder to find. So, a tank would need to hold 2000 divided by 3 gallons, which is 667 gallons.

The can looks to be about twice as high as it is wide so the height is four times the radius. So the radius is 46.5 inches, the height is 186 inches. Therefore, the volume is 5,470 gallons. While this number may seem precise, it is not in fact very accurate because of all the estimating that was done to arrive at it. Nonetheless, it appears that the tank is more than sufficient in terms of holding enough water to extinguish a house fire many times over.

Q2. Your task: work on this puzzle yourself, and let your 'teacher bird' and 'student bird' notice how you approach it, where you can use reasoning and where you need to research, where you get stuck and un-stuck.  

My teacher bird always seems to take a backseat to my student bird, as was the case with this problem. I approached it with a mixture of educated guessing, unreliable google research, and with consideration for the real-world context of the problem. This type of problem reminds me of the type of questions that come up while building things and planning/designing, which is always fun. I got stuck looking for the exact dimensions of a Campbell’s soup can because the only dimensions that I found were 51cm by 61cm but that can’t be right because it looks much taller than that ratio of width to height.

Q3. Then work on either: (a) extending this puzzle, or (b) coming up with your own puzzle for secondary math students based on a real-life observation you have made (and include a photo or graphic to support it).

I think it would be interesting to extend this puzzle to consider how much soup that would be if it was actually full of soup. 5, 470 gallons of soup, how long would that last if you ate a big bowl of soup every day for lunch. How many tomatoes would go into making 5,470 gallons of tomato soup? How much would that many tomatoes cost compared to how much would that much soup cost? What if we buy in bulk?