I used to think maybe they were open at the top and caught rain water and stored it. But then there would be birds and stuff getting in there. And we're drinking that? Luckily how I thought they worked isn't at all how they work. You can read last weeks blog for some basic info on how they do in fact work.
Here is a great example of a math application. It is a combination cone and cylinder. I tried to blow it up so you can see the numbers. Of course you can simply make up problems with numbers, but its nice to have numbers of an actual thing - even if the thing is just a picture from the internet.Our town has a cylindrical water tower whose base sits on the ground. A good project would be to estimate the number of gallons it would hold. You could estimate the the diameter by first pacing off the circumference and then doing a little math. Then you could just estimate the height by eyeballing it, or better yet, doing some trigonometry. Granted, it would be a pretty rough estimate, but a nice project. I'm sure the water department, or someone, has the actual numbers. You could then get those and compare your estimate to what they say.
I saw a company on-line that said they had towers, "Available in diameters from 11 feet (3.3 m) to 204 feet (62.2 m) and capacity from 20,000 gallons (75 cu m) to over 6 million gallons (22,700 cu m)". They are the self-proclaimed "premium water and liquid storage technology leader", so they must know their stuff.
This is a picture from their website. Oddly they don't mention the height, So a question might be: For a given diameter, say 50 feet, what height would be necessary to have a 100,000 gallon tank? I looked up the fact that there are 7.48 cubic feet in a gallon. There you go. A great application.
A look on line shows that there are certain fairly standard shapes, but quite a few atypical designs, lending themselves to using several different volume formulas.
