To be Devil’s Advocate:
Given that the rest written in Comic Sans, it may be an early elementary school exercise, aimed at teaching kids to do multiplications. In this case, it’s tolerable and/or defensible to find a simplification for pi.
That said, making pi equal to 3 would have been more accurate for that…
Depends on the level of precision you need. If I want the volume in a 500 foot long, 3 inch pipe to roughly estimate how much supply I need to order, I wouldn’t need a calculator. It would very roughly be 90-95 ft3. (Divide 500 by 4 two times and multiple by 3)
Then I would spend 5 minutes double checking myself haha.
In astronomy, pi=1 or 10, depending on whether you’re trying to over or under estimate something. Because when you’re trying to estimate distances measured in millions of light years, the difference between 3 and 10 is just one or two orders of magnitude on a small number. It’s pretty common for astronomers to do napkin math by rounding every single number to the nearest zero. 91k becomes 100k for instance. Because the napkin math estimations are just trying to gauge whether some celestial event or object is a thousand light years away, ten thousand, a hundred thousand, etc… And pi becomes 10, because that’s the nearest round number.
…if they’re above average, I think they’ll figure out the explicitly defined variable. I think the instructor is trying to make sure this problem doesn’t require a calculator and figured defining pi as 5 makes it clear that you can treat it as a whole number. 3 would be more accurate and just as easy, but meh idk that this is that great of a blunder.
You can be a smart kid and not realize that adults are lying.
I remember the Peas and the Punnett Square. Sure, mendelian genetics explains pea plant colors, but doesn’t explain dog fur colors. Just providing a footnote that more completed genetics exists would have been nice.
Or it’s from an ME. They seldom can remember the rounded value of Pi, but they’re pretty sure it’s somewhere between 3 and 4. But you probably should use 5 just to be safe…
Good thing I don’t need to do math at work. Saw a video the other day where someone said “10x400” and was shocked that they couldn’t instantly multiply by a power of ten. And then I walked into this.
If you really wanted to be through you’d start at a point, integrate out along dr for a line, then integrate in a circle through dtheta to derive the area before doing the rest
Nobody knows how to think like a dyscalculic at all haha… it’s just a little symbol thingy… it doesn’t have to be pi. Just like X is a little symbol thingy… the x is now just kind of a table right now… it’s just a little symbol thingy and it means five it’s not that difficult. Lmao
Yes it does have to be pi because that’s the formula for the volume of a cylinder. If you take a simple, cylindrical glass or container and measure it and apply the formula with pi, you’ll see that you’ll get the correct volume of the container. If you just want your kids to calculate a random x that’s 5* 10 *10 *10 just tell them to do that, don’t give them a made up formula, it’s not that difficult.
Mathematically, no, it does not. We make up the definitions. If you wanted to see what the consequences of a, I don’t know, 5-dimensional universe with Pi set to 5.65 were, you can do that. These are scribbles on pages, there is literally nothing stopping you.
Academically, what’s stopping you is whether these calculations are useful. The only problem I see here is that it’s kind of misleading to imply to someone that Pi is something it conventionally isn’t. But even then, I think I’d respect the mathematician who could recognize Pi as a symbolic name for, usually, one particular transcendental constant a little bit more than one who refused to even entertain the idea. Like, imagination is important to mathematics, too.
And to be clear, “let Pi = 3.14” is also incorrect. It is closer than 5, but it is still infinitely wrong.
[edit] And also, I was imagining this question was for a younger audience. Reading it again, I’m not going to pretend I know what’s going on up there.
I think you’re overthinking it. The first thing you’re told when you learn algebra is that a letter represents a number and you can say “let a equal (number), b equal (number)…” so you can let pi equal whatever you want for the purposes of one simple problem.
Except pi isn’t a variable. It is a known value that we refer to as pi for convenience, and pi is a fundamental aspect of how a circle is. Saying “let pi equal 5” is all fine and well but is physically impossible, you will not be determining the volume of a cylinder if you let pi equal 5, because the ratio of a circle does not equal 5, it equals 3.14
But I suppose part of solving a maths problem is staying within the confines of the question and listening to instructions, so if someone says “using pi equals 5”, I’d just use pi equals five and take my point with grace.
Well, if we want to be pedantic, they never said that h is the height and r is the radius of the base circle. They could be just random numbers.
Also, since we never calculate with all the digits of pi, it is not any less weird to round to the nearest 5 and say that it’s 5, than to the nearest 0.01 and saying it’s 3.14. It just has a higher amount of rounding error.
I think it’s actually a very interesting question. Pi does not equal 5 in our universe, but perhaps we can think of a meaningful universe where it does? Perhaps some mathematicians/physicists can chime in?
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