The Giant Soup Can of Hornby Island

The problem: given the size of the actual Campbell's Soup can (of normal size) and the height of the bike in the photo (my own medium-sized hybrid bike), 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?

 

My thought process:

1) How tall is the large can?

Given a "medium sized hybrid bike" and that a bike's height typically comes up to someone's waist, I'd guess the bike is about 3 ft from ground to saddle.  Then the left side of the can looks to be about 3 saddles tall -> around 9 ft.  The right side seems to be a bit shorter, maybe 7-8 ft.  Since the slope seems pretty steady, I'll just assume a regular cylinder with an 8 ft diameter for ease.

2) What are the details of the regular Campbell's soup can?

According to the internet, a soup can has a height of 4.5 inches and a diameter of 3 inches for a 10.75 oz can (based on images).  Based on a soup can I measured, it has a height of 4 inches and a diameter of 2.5 inches for a 284 mL (~9.6 oz) can.  I'll go with the one I measured in case the internet is lying to me.

3) What is the proportion between the cans?

If the small can has a diameter of 2.5 inches ~ 0.2 ft and the large can has a diameter of 8 ft, the large one is 40 times the small one.  Then it's easy to say that the length of the large can should be about 40 * 4 in = 160 in ~ 13.3 ft.  Based on looking at the width of the bike (4-5 ft?), this doesn't seem like a crazy number.

4) What is the volume of the large can?

If it has diameter 8 ft, then it has radius of 4 ft.  So the cylinder is pi*(4 ft)^2 * (13.3 ft) ~ 670 ft^3 ~ 19,000 L ~ 4,173 G.  You could fit ~130 of these into an Olympic size swimming pool, which also feels okay as a guesstimate.

5) Does it hold enough water to put out an average house fire?

Google has some quite conflicting numbers for the water needed for an "average house fire," ranging from 300 gallons to 3,000 gallons.  Either way, it appears that the soup can does hold enough water.

 

Thinking about my process:

For one, there were a couple parts where Google told me something that I then decided to go off my own knowledge instead: how tall a bike is, how tall a soup can is.  However, I genuinely had no idea how much water is needed for a fire, so I was forced to accept what was given to me there.

In basically every step, I fact checked whether or not I felt my number was reasonable (both with a friend and with a comparison to something else).  I tend to be bad at feeling out how big a random number is, so comparing to something that I've actually seen is very helpful for me.  I think that one of the most valuable parts of estimating something is checking whether or not what you have makes sense.

I briefly got stuck on when I thought about the ratios: I was thinking that I could just use the volume of the small can to get the volume of the big one (and you should be able to), but I tend to get confused when converting area/volumes through ratios, so I figured it would be best to just recalculate it.  In fact, if you go off the 284 mL volume of the can and multiply it by 40^3, you get about 18,000 L which is now another way to double check my math.

 

Going beyond— a new puzzle:

Something that I've found people enjoy in the past is the similar question: How many of [this] would fit in [that]?

A basic example: The room occupancy is [x], but if we didn't care about personal space, how many people do you think could fit in the room?  In this universe, people can fly.  How about cats?  How about ants? 

(no picture since the classroom you are in would be most applicable) 

A classic: How many [candy] are in the jar?

 

Not real life, but kind of fun: If we were in a zombie apocalypse, is there a vehicle that we could all successfully get away in?  

Further restrictions can include: 

- I must be able to drive it without practice (ie. no trucks etc)

- What's the smallest one we could get away in?

- Okay, we're driving across the country so maybe we all need some personal space.  What now?