Assuming the water tank is cylindrical in shape, and assuming it has the same proportions as a can of Campbell's tomato soup...
*The second assumption allows us to approximate the volume of the tank without needing to approximately measure both its length and radius.
V = pi*r^2*h (where h is the height/length of a cylinder)
We now just need to find how many times larger the length of the water tank is relative to the length of a soup can.
Length of the water tank:
We can use the image provided to approximate the length of the water tank. This process will first involve approximating the length of the bike in the picture. We will then use this to find a value for the scale of each pixel in the image, which can then be used to measure the length of the water tank.
*Research can be done to try to find the exact length of the bike. for example, based on the logo and shape of the frame, the bike appears to be some version of a Norco XFR Stepthru model. However, short of tracking down the owner of the bike, it is impossible to be certain of the bike's sizing, as well as the specific details of the wheels/tires. For these reasons, we will instead take an approximate average bike length of 175cm, based on Carl Ellis' article, "What size shed do I need for my bikes?" from thebestbikelock.com.
The image was opened using ms paint and the x-coordinates of pixels on opposite ends of the bike and water tank were used to approximate lengths. This gives the water tank an approximate length of 432 cm.
Height of a Campbell's tomato soup can:
Taking measurements from campbellsfoodservice.com we find the height of a "typical" can to be about 4-inches, or 10.16 cm.
*Here, we're assuming that these advertised measurements would be the same as the vintage soup can depicted on the water tank. It likely that the dimensions of Campbell's soup cans have changed over time, and as this work is a reference to Andy Warhol's paintings, we might attempt to track down a can from the early 60's and measure it ourselves for the sake of "accuracy." Instead, we will use the 4-inches, which is itself an approximation as the 4.125 inches on the website likely includes the thickness of the cardboard box in which the cans are delivered.
Ratio of the length and the height:
Dividing the length of the water tank by the height of a soup can...
432 cm ÷ 10.16 cm = 42.5 times larger (approximately)
Volume of the water tank:
V = pi*(42.5r)^2*(42.5h)
V = 76765.625*(pi*r^2*h)
Having used the length/height instead of the radius, and again working with the assumption that the dimensions of the soup can would be the same as those of the water tank (assumed to be cylindrical)... It follows, from the volume formula of a cylinder, that the water tank's volume will be about 76766 times greater than that of a "typical" Cambell's soup can. Again from, campbellsfoodservice.com we have a volume of 10.75 oz (assumed to be US food label fluid ounces) or 322.5 mL
322.5 mL * 76765.625 = 24757 L
Since there was so much approximating anyway, giving a final approximate answer of "about 25000 liters or so" feels appropriate.
Is this enough to put out an average house fire?
From a linkedin post by DryTech Water Damage Restoration Services titled "How Many Gallons Does It Take To Put A Building Fire Out?" we see that it is "fairly normal" for fire departments in rural areas employ water tanks that carry between 1500 - 3000 gallons of water. Converting this to liters, we have a rough estimate of 5678 - 11356 liters water being a "fairly normal" size of water tank with which rural fire fighters would arrive on the scene and expect to extinguish a typical fire.
*There is a lot of guess work in this problem. As a student, I can see it being both interesting and frustrating to play detective and wrestle with how much research are you willing to do vs. how many assumptions/approximations are you willing to make. One could obviously take it a step further in either direction, and/or work from different assumptions. One might also choose to work with small and large estimates in order to get a range of values for the answer. As a teacher, I think whether or not the student is able to accurately estimate the volume of the tank is one thing, but it's probably more interesting just to note how a given student approaches a problem like this. I think you might get a student who enjoys the challenge of being as accurate as possible, and consequently, does lots of research and justification of their method. On the other hand, you might get a student who is much more willing to estimate without putting too much time into it, and that is also valid. Math wise, I would especially want students to be aware of how the scale factor of a single dimension would affect the scaling of the volume, and being able to connect that to volume formulas. In other words, I would want to see students aware of how scaling volume will essentially have you cubing your scale factor.
Because so much of this puzzle involves research/assumptions/approximations, I think the natural extension would be to make it explicitly clear to students that you want them to do research, citing their sources, and justifying their usage of them.
Beautifully written and explained, Mark! I like your reflections about the approaches of problem-solvers who love accuracy and those who are willing to live with a degree of uncertainty; we certainly encounter both these approaches in math classes! I would think that asking students to be explicit about their research would be part of the original question, so I don't really see an extension here -- if you'd like to go from a '2' to a '3' for this post, perhaps add an *EDIT* adding a more distinct extension idea!
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