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NationalTutoringObservatory
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MathEd-PII

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8
student
All right. Can you um delete the board?
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volunteer
Sure
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student
OK, so I found the like cause I told you I already have a big test coming up like give out, um, related rates and um global minimums and maximums and stuff. But um since we're, we're working with like related rates today, I found like a midterm, like a, like a sample.
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student
Uh, so
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volunteer
OK
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student
but he has like different parts to it. So this is like the first part. It has like the
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volunteer
Yeah
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student
question and he has like stuff that we have to go through like questions you have like
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student
letters A to
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volunteer
Go
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student
E. OK, but they're not like a lot, so.
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volunteer
I'm, yeah, I think it, it seems similar.
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student
for the first one to read and I read.
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volunteer
I'm sorry, say again
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student
No, you can go ahead
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volunteer
Anyhow, it's, it's not unlike what we were just doing.
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volunteer
from the looks of it
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volunteer
We're, we're
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student
Yes
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volunteer
it's, it's very similar to the problem we just
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volunteer
did, and they're all kind of have a theme to them.
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volunteer
So let me see what this one says.
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volunteer
Mhm
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volunteer
Right
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volunteer
Right
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student
OK, but on this one, since, uh, I kind of want you to like, I kind of want myself to go through like everything and then uh whenever like I'm make a mistake, then you can be like, oh, that's not correct. Uh, and then if I have a question, I'll just ask you, but I really want to go through all of them.
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student
Yeah
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volunteer
Yeah, definitely, uh, definitely.
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volunteer
So, I'm just gonna read the first part here.
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student
Yeah, I'll read it
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volunteer
OK.
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volunteer
I'll read it out loud. The cylinder is changing size in such a way that the volume remains constant 12 pi cubic meters.
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volunteer
Denote the radius of the cylinder by R and the height of the cylinder by H.
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volunteer
and the area of the circle at the top of the cylinder
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volunteer
by
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student
OK
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volunteer
kind of stops there. That's kind of weird.
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volunteer
OK.
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volunteer
by A. OK, I see it.
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volunteer
All right.
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volunteer
So
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volunteer
I'll let you go ahead and
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student
OK
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volunteer
go ahead and uh
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volunteer
start working it
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student
OK, so for letter H, turn this back, it says that uh live with the diagram with the length R and H so draw something on the diagram.
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volunteer
Mhm.
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student
It's kind of small here but
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student
yeah
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student
OK it says RNH do I also have to like add the volume, I mean, the the values or no? Just keep it at that.
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volunteer
Say again, ask that again, please.
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student
So I'm saying like it says labels with links R and H, so doesn't want me to also add the
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student
the, the, the values of the age.
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volunteer
Um, I don't think so.
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volunteer
at this point
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student
Yeah, since you said RNA.
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student
Yeah
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volunteer
So you did that just fine, yeah.
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student
OK
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student
OK, I'll just write what we know because it makes it easier. So we know the volume
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student
Oh sure.
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student
By the way, you can stop me whenever I'm doing something wrong.
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volunteer
OK
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volunteer
So
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student
So
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student
OK.
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volunteer
um
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volunteer
what you're doing is fine, but if you're going down to point B, I
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volunteer
you know, that's what the next step they tell you to do, right? So.
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volunteer
Exactly. That's great
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volunteer
Yup
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student
Yeah, I'm just writing it down so like I have it in my head and I can see I can picture it cause that's what the pro uh it uh the teacher also tells us to do.
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volunteer
Mhm
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student
OK, since I see that we have the like the volume. I'm guessing that for the formula, we're gonna have to find like the.
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student
something um either with the volume or the area cause we're trying to find the
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student
area, but we had the volume, so maybe you need to find like both um formulas and like introduce it, if you get what I'm saying.
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volunteer
Yes
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student
OK, I for I forget what the um formula of the um volume for the cylinders. Is it H times
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student
uh
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student
it's.
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student
pi R
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volunteer
I heard you say it
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volunteer
Yup
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student
2 times age.
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volunteer
So think of it as slight, think of that as a as a piece of cheese around cylindrical piece of cheese.
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volunteer
You, you have cross sections which are circles, right?
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student
Yeah.
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volunteer
And if you, if you slice it
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volunteer
you could just
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volunteer
think of multiplying
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volunteer
the height times the area.
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volunteer
sort of uh, but that's the same thing as piR2H and so I think
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volunteer
you're
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volunteer
you will have no problem remembering that.
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student
I hope.
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volunteer
Mhm
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student
Mm
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student
OK, so do we also have to know the um
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student
the area of a cylinder, like the formula of the area of a cylinder.
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volunteer
Well
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