Keeping with the easy definition of “real world” being “math someone needed to do at their job” – I actually prefer the term “industry math”, but regardless here’s the question that needed to be answered:
My wife’s working on a project where they are building a house on a property without a well or access to city water. So they dug a 425ft well that was 8 inch in diameter. When they finished the dig at 3:00 pm it was completely dry. The next day, at 7:00 am, the well had filled with water up to 45ft below the surface.
How fast is the well filling up in gallons per minute?
They wanted 1.25 gallons per minute. Do they need to dig another well? Wells are about $50 a foot – so yeah, they would rather not dig another one.
(digging the well)
(well finished! That’s the cap they left on it)
They used a falling rock to determine how much of the well had filled with water. Well (not the noun), they also used a cell phone connected to a string but isn’t that just too obvious?
Here’s the video of the rock drop:
Well Rock Drop
I just can’t type “real-life” without quotes because I’m yet to resolve what “real-life” means in a math class. But for this post it means – “Math someone needed to do at their job”. And in this post that someone is my wife – who much to her distain and my joy – does a lot of geometry as a project manager at a construction firm.
So here’s what we need to know: How much cement is needed to make that border? We need the answer in cubic yards because you buy cement in cubic yards.
The image below provides some of the context for the problem – The cement border is being used to circle an existing tree.
I was actually surprised how open the middle was on this problem. Yet students used two main strategies. The first was the standard subtract the areas and multiply by the height, or they subtracted the volumes of both cylinders directly. The second was the find the perimeter, think of the wall as a rectangle (dimensions of 2*pi*r X 1′), find the area of that rectangle and then multiply by the height.
One student using the second strategy used a radius of 14ft and got a solution of 16.2 cubic yards. He told me he knew the answer would be a little too small because of only using the inner radius. Another students used 14.5 and got the same solution as the area subtracting syndicate.
Converting from cubic feet to cubic yards is a great time to practice your perplexed I wonder why you divide by 27? face.
By the way the wall ended up costing around $35000. I can’t believe how long I would have to work to put a wall around a tree 🙁
Posted in #industry, #technology, geometry
Tagged annulus, area, cylinders, geometry, industry, IndustryMath, math1, math2, open middle, real-world, volume