For all the discussion on tank volume dipstick depth, a simple google search turned up a no math no sweat calculator. http://www.greertank.com/tankcalc.htm gives you all the info by entering 2 numbers and shows volume at every inch of dipstick depth
And anybody with a 8th grade math level can figure it out with a pencil and paper. It’s NOT complicated math.
I agree, and I’m trying to think when I need it. The only tanks I have w/o gauges are those on outboards , chain saws, lawn mowers etc. and none has a completely cylindrical or rectangular prism shaped tanks. Generator does but that has a gauge. The translucent ones have marks on the side. Guess I missed all the discussions, sorry.
MikeInNH: Please to be showing your work using 8th grade math. Thank you.
V=lwh for a rec. prism, Pi times r^2 times h for a cylinder. In cubic inches, that volume divided by 231, the number of cubic inches in a gallon, would give you the number of “segments per gallon” for each container along it’s height (depending on orientation). Then divide into the actual height in inches to calibrate the marks on the dipstick. The procedure may have to be walked through for an 8th grader, but I would hope they can all multiply and divide and understand the process and apply it again when finished. This basic procedure depends on the orientation of the solid and where the filler hole is…a cylinder on it’s side is different and adds a little more math. Which I might add, today’s 8th graders may/not to be exposed to.
Otherwise, without speaking for “Mike”…that’s well within an average 8th grade math w/o a calculator.
If you’ve noticed dipsticks on containers with marks that are not the same distance apart, you “know” the containers are irregular and/or cylindrical(curved) along their height. That starts to go beyond basic math and includes higher math. Of course, given time, the tank and water and trial and error and a gallon/quart container off to the side; you can come up with a pretty close estimate for the marks on a dip stick for just about anything…a 6 th grader can do that.
First, “The procedure may have to be walked through for an 8th grader” which means it’s not eighth grade math.
Second, this approach only works if the height (the axis perpendicular to the circular bases) of the cylinder is aligned vertically. Second(a), please to be finding a truck where the fuel tanks are so oriented. Second(b), the whole point of the Puzzler was that the cylinder was oriented so that its height was oriented horizontally.
I am unimpressed by bold.
“This basic procedure depends on the orientation of the solid and where the filler hole is…a cylinder on it’s[sic; 8th grade English] side is different and adds a little more math. Which I might add, today’s 8th graders may/not to be [sic; I mean “what?”] exposed to.”
Hence, not 8th grade math. Please to be specifying “a little more math.”
"Second, this approach only works if the height (the axis perpendicular to the circular bases) of the cylinder is aligned vertically. "
-I believe that’s what I said…and the discussion was only about the math, not the tanks orientation.
-Yes it is 8th grade math if you teach it and they can then solve similar problems on their own; otherwise it would be called 7th grade math if they knew it already.
-The bold obviously did make an impression; you commented on it !
-You could use ratios and proportions to determiner the mark locations after you found the height (oriented horizontally) of a segment of the tank that contained half the volume, then 3/4 for example.
-you could use Trig. to find the relative height of any segment that represented a distance between two marks with respect to the angle formed by the radius and that segment length. If I remember, sin 45 = Height (above halfway mark)/radius (known) for volume of 3/4 of total. Solve h = one mark…now you have 0,1/4. 1/2, 3/4 and full marks. Simple Trig functions as a supplement to beginning algebra is done in some 8th grade classes
-You talk 8th grade math like it’s all the same; there are different skill levels and I still agree that Mike is right esp. given that estimation skills in basic math as emphasized by the bold (you were impressed with) is a valid approach too. Heck, we used this 6th grade math skill all the time as a verification approach to volumes and areas in calculus.
And yes, though I can’t remember much else even you or I could do that.
“You talk 8th grade math like it’s all the same…”
No, I don’t. I simply asked to see the math. You’re the one who said 8th graders could use your solution, which doesn’t even solve the original problem, if you “walked [them] through” it.
“-I believe that’s what I said…and the discussion was only about the math, not the tanks orientation.”
When did this become the Solid Geometry Ignore the Real World and Original Puzzler discussion board? I missed that memo.
“-Yes it is 8th grade math if you teach it and they can then solve similar problems on their own; otherwise it would be called 7th grade math if they knew it already.”
So at the beginning of 9th grade a student knows math only up to the 7th grade level? Gotcha.
And your teaching experience is…
Guys, are we really arguing about whether math is at an 8th grade level or not? This discussion is at about a 3rd grade level.
I’m not arguing at all. Neither is Mike in NH. I’m sure if Dagosa (who jumped in with nonsense, not to be confused with Louis Armstrong’s Struttin’ With Some Barbecue) were here, he-she would say "And your teaching experience is… "
Now somebody send our trucker friend this link before he runs out of fuel!
It is nonsense if you can’t follow the math. If you have only your own learning experience, you may never have been exposed to problems like this. If you had classroom teaching exp.and used a discovery method, varied approaches would make sense, and yes some could use algebra, trig and/or sampling. Many schools now introduce algebra at very early, stages. Not all kids can use it for this problem, but given time and resources, it’s still 8th grade math problem. I don’t know about your schools, but kids in many schools are sitting there with a lap top.
BTW, if we’re not doing problems like this in most 8th grade math classes, it will be a tough time improving our world ranking in engineer graduation rates.
And, why can’t you start with an empty tank and start filling it up a quart/gallon at a time and put your observed marks on the dipstick. Tell me an 8th grader couldn’t do that.
He’ll think he’s listening to Amos & Andy!
An eighth grader could do that 24/7/365, but it wouldn’t solve the Puzzler, unless you’re positing a truck with cylindrical tanks oriented so the height of the tanks is vertical. I pointed this out before. Please try to follow along.
“but given time and resources, it’s still 8th grade math problem.”
Given time and resources, you can teach an 8th grader calculus. And a sewer rat might taste like pumpkin pie, but I’ll never know (you can google that to read how it turns out).
“BTW, if we’re not doing problems like this in most 8th grade math classes, it will be a tough time improving our world ranking in engineer graduation rates.
And, why can’t you start with an empty tank and start filling it up a quart/gallon at a time and put your observed marks on the dipstick. Tell me an 8th grader couldn’t do that.”
Given that you assume a tank whose height is along the vertical axis, why bother with the extraneous step of putting fuel in the tank at all? Why not just measure the height of the cylinder and divide by four? That’s what a good teacher would suggest. Why are you wasting your students’ time? There. Your solution, which doesn’t solve the Puzzler, not only isn’t 8th grade math, it doesn’t even require math beyond the first grade level. Most importanly though, your solution has nothing to do with the Puzzler.
And your teaching experience is…
I posed the problem to my youngest who’s in 9th grade…and it took him about 5 minutes to solve.
Yes there are 8th graders who many not be able to do the calculation…but that doesn’t mean it’s not taught. The point I was making when I said it was 8th grade math…is that the math to solve this problem is taught in 8th grade…OBVIOUSLY there will be many 8th grade students who can’t solve the problem. But figuring out volume is taught in 7th and 8th grade. You don’t need Algebra or Trig or Calc…Simple arithmetic is all that’s needed.
tarcault "Why not just measure the height of the cylinder and divide by four? That’s what a good teacher would suggest. "
A good teacher would not suggest anything.
And I believe you dismissed that idea as the tank was on it’s side and dividing by 4 with a cylinder doesn’t do that. As Mike rightfully stated, you don’t “need” Algebra, or Trig or Calculus or…what ever you want to put in there. The teaching strategy in problem solving is to not just find the answer, but show how the solution was found in several different ways and let the student discover. We then use that as an opportunity to teach algebra, trig, calculus etc. as the students suggest an approach. Students find many unique ways in approaching these problems instead of imitating a predetermined method.
And I still agree with Mike…It’s a good 8th grade problem.
"There. Your solution, which doesn’t solve the Puzzler, not only isn’t 8th grade math, it doesn’t even require math beyond the first grade level. "
The discussion had nothing to do with solving the puzzle; it was around 8th graders doing math to solve it. ANY problem solving method can be developed in a math class to solve problems, it does not have to agree with your or my idea of what computation skills are or are not required. Your curriculum development ideas short change our kids. 37 years.
Guys, pay attention the answer is at the top. 3 clicks, no thought. Even you guys can do this one.