@neilmurfin7775 Thanks Mr. Murf I learnt from the best.

literally me rn istfg

@@cyover4401 fr, mine is due in 2 days lol

I love it.

Ya exactly.

Ya a volume of revolution IA involving some medical product. Maybe a tablet or something 3d printed. You'll have to find something. I have also had in the past a very good IA modelling the ECG of a healthy heart and an unhealthy heart. He then looked at the area under the curves and compared. There is lots of data out there that you can use to create a model. Like number of covid cases or hospitalisations, etc. Hope that helps.

I have samples including this topic on my website. Behind the paywall sorry.

You can do all that and it sounds good but the important part is to show your understanding throughout the IA. Don't do anything you don't fully understand.

The online version. Just go to geogebra.org and it's there.

Yes to the first question. And sorry, I am not familiar enough with Lagrange multipliers to advise you.

Sorry I'm not sure what method is used. Let me know if you find out.

The Temple of Heaven looks like a very good one. Why can't you use it? It has to be a solid of revolution if you want to use this process. The Burj Khalifa is not one so wouldn't really work. The new Dubai Creek Tower (which will be the tallest in the world) would work. Otherwise I'm sure there are plenty more out there which would work well.

Sounds good but you are correct, you will need to find the right shape. It won't work for a normal gummy bear.

Yes. Sounds good. The water idea sounds fine to me but remember your teacher is marking it so listen to their advice. I have a video on volume of revolution on my website but I'm sure there are plenty KZfaq videos too that explain how to do it.

Yes it does.

Try this link www.geogebra.org/classic#3d

What do you want to design?

@@MrFlynnIB I looked at several options such as a watering can or a bottle but I could not think of any particular purpose for the redesign or an aim for the investigation (optimizing the surface area so that the costs/ environmental impact can be minimized has already been done a lot of times so I wanted something unique)

Sounds good provided he is the right shape. Can you model him using a solid of revolution?

I don't think this works. A solid of revolution has particular properties. It is formed by rotating a curve around an axis. I don't think a barbie doll could be modelled well using this. Sorry. A good idea for you maybe (beauty and volume) might be to find the volume of a 'beauty blender' sponge. Apparently the volume doubles when it gets wet so you could test if this is true.

Is this a joke?

@@MrFlynnIB Or maybe can I apply it using integrals? and measure the area?

@@fernandallanosm Yes this IA would work better in 2d. You could model the shape of the barbie using functions. You probably know what to do better than me after this. Maybe look if this shape is even healthy for a human.

​@@MrFlynnIB Hi MrFlynn, I really like the idea about the beauty blender, and I want to explore this in my IA, I would like to know if I should go ahead with it, and if so, what advice would you give me in my process? D you think this could earn me a 7 as an sl math ai student?

You will need to use the volume of revolution formula. It's in the formula booklet.

@@MrFlynnIB Hello, Can I keep the height as a constant and find the radius of the bottom and radius of top of the object and use integration to find the volume?

@@nayelnayel865 Isn't this the same as what I did?

There is a formula in the formula booklet. Use that. All you have to do is sub in your function.

my tteacher said to post a screenshot of geogebra exporting the function

Nevermind found it already, anyone else who face the same trouble as mine, try using geogebra classic 6.

@@arianaazmir4321 where do u find geogebra classic 6?

Sounds like a rounding issue. Change the number of significant figures displayed in geogebra.

@@MrFlynnIB that seems to have fixed it, thanks so much.

It's just a quick way of changing the degree of the polynomial function. So if n=2, it is a quadratic, if n=3, it is a cubic etc. Let me know if that doesn't make sense. You don't have to use it, just put a number instead of n.

@@MrFlynnIB Oh I understand! Thank you. Just another quick question, how did you decide the size of the picture? I guess you based it on it's real life measurement if I got it correctly. Thank you again.

@@eb5141 Yes, real life measurement.

Sometimes it won't fit a particular function because of where the points are. Geogebra can sometimes be a bit finicky/annoying. Try moving the points and try again.

Geogebra is only showing 0x^4 but really it 0.something which you can't see but which is important. If you change the number of decimal places, then you can see the extra numbers. I show how to do this in my bitcoin video.

@@MrFlynnIB thank u very much. ill look up your bitcoin right away

Sorry I don't understand this question.

This is a good and not an easy question. One thing you should calculate is the R squared value. Geogebra can also do this. The closer to 1, then the better the fit. However, you have to be careful as higher degree polynomials will always fit better than lower degree ones. But it doesn't mean that this is the best model. For example, check out my basketball shot video. A cubic or quintic model would actually have fit the data better but a quadratic is obviously the better model for a basketball shot. As a fairly general rule, with polynomials, you want the least degree that still fits the points well. Hope that helps. Just make sure that you justify your model and explain why you chose it. This will help with reflection and understanding.

@@MrFlynnIB That makes sense. Another question I had when doing it was would I have to explain what polynomial regression is because geogebra created the line? Because polynomial regression is quite confusing or could I just state geogebra calculated the fit and which degree was the best?

@@arnikumar5407 You don't need to sow the polynomial regression. Yes, that gets really complicated. What you have to do which is important is justify why you chose that model and talk about goodness of fit.

No, just one. Then rotate it 360 degrees around the x-axis.

I think you could find better. I think even the regular gatorade bottle would be more suitable.

@@MrFlynnIB Thank you for replying, sir. Yes I agree that a gatorade bottle would be a better suitor but however, whenever I think of an object that has the rules of the solids of revolution, I can only think of bottles, and vases. So the gatorade bottle (twist top one), for me has more than 5 functions I could model it on. I want to be an industrial designer so I will relate it to how companies are able to model a bottle with abstract functions, but able to have a consistent volume within their bottle. Would this aim and object still be good? If not can you recommend any other objects I could do it on

@@MrFlynnIB Also since I am in SL, would I need to derive the formula for Solids of revolution? Since its not in the syllabus, however it is in my textbook

Yes this would work. Check out my IA guide. Lots of ideas in there.

Yes for sure. That isn't a problem but make sure you explain what you doing well enough that an SL student in your class can understand it.

@@MrFlynnIB Thank you so much!

This example is revolved around the x axis but you can revolve around the y axis too.

No good reason. I probably shouldn't have.

@@MrFlynnIB Ok! Also, would this be enough for an HL IA? The IA has to be 12-20 pages I believe and I'm not sure if I will have enough to fill up that many pages :(

@@kellyjin2469 I have seen many IAs on this topic in the 12-20 page range. Some done well. Some done not well.

@@MrFlynnIB Thank you! Also, the best fit function shows up on GeoGebra correct?

@@kellyjin2469 you have to tell Geogebra which function to try and fit and then Geogebra will find the function of that type that best fits the points you give it.

There is a formula in the formula booklet.

Yes.

@@MrFlynnIB I mean, for an object that is for instance like a round teddy bear. Also would it be too difficult to find the minimum surface area of revolution? and how would one go about it.

@@allysona843 You could find the surface area of revolution. There is a formula. To find the minimum surface area is different. What does minimum surface area mean in this case? Are you going to change the shape of the bear?

You need to find an object that is a solid of revolution for which you want to find the volume. A good example that I have seen (maybe I mentioned it in the video) was a beauty blender sponge. Apparently the volume of this sponge doubles when it is wet. One of my students wanted to find out if this was true so she used this topic.

@@MrFlynnIB Would measuring the volume versus the surface area of the bottles of sprite and Coca-Cola to see which optimizes the use of plastic be a good topic for AA HL?

@@karimkhaddour4720 Ya not bad but really you know the volume as it says it on the label (unless you aim to verify this) so really it would be more about finding the surface area to see which is smaller. Which works fine.

@@MrFlynnIB Do you think i could use this as well and if so what would the rq be does the volume of a beauty blender double when getting wet?

@@sunniva7786 Remember it is an aim, not a research question. But ya, that sounds like a good aim.

You could do either. Or both. Depends what you want the aim of your IA to be. Try to find a reason for getting the volume or surface area.

@@MrFlynnIB Could I say I want to use the volume to know to know the quantity of soap that can be put in? Thanks for the reply

Ya I guess that works.

geogebra.org it's online and free.

Yes to both. Sounds good.

Yes. There is also a formula for surface area of a revolution. It is not in the formula booklet but easily found online.

@@MrFlynnIB i see but can i use this f(x) equation for the surface area of revolution as well

@@StrawberryS-vk5my yes.

I meant talk about how well the function fits the curve. The R squared value is one measure but be sure not to solely rely on this.

Ya but find something interesting to get the volume on. And a week is not a lot of time. Let me know how you get on.

@@MrFlynnIB thinking of doing the volume of funko pop

@@gokupods4088 It's not really a solid of revolution so won't work well.

Do you recommend volumes of revolution or modelling (bitcoin, for example)?

Yes it is a good topic. Volume of revolution is not in the SL course so good for HL.

Both are good ideas. I would choose the one that interests you more.

@@MrFlynnIB Thank you sir. I was thinking of modellating the sea level rise along time. Since I am in AA HL, would it be a good idea to get the line of tendency manually instead of using Excell/Geogebra (with the proofs of the statements I use, which some of them include calculus)?

@@mateogullon3092 What kind of model are you think of using? Linear? I could work but generally I don't recommend this for HL.

Try to think of a good reason why you want to find the volume. Does it have to be a vase? I would take my own photo if possible.

Yes. Note: it is not in the syllabus so you will need to explain it as if the reader has never heard of it.

@@MrFlynnIB hi sir, how would one approach it? Do we just explain the concept or also the math like in the textbook?

@@nasirahmad7792 Watch my 8 part IA guide. This will give you a good idea of what is expected.

Thanks. Glad they are useful. A decent online calculator should be able to do what you need. Try desmos.com.

Haha not sure. Maybe I was having a bad day. Ya absolutely for the coke bottle.

@@MrFlynnIB any idea how I would determine the surface area of the coke bottle? I was thinking about doing an optimization IA (volume o surface area) for HL

@@marcusb.7412 There is a surface of revolution formula that you can use. It is not in the syllabus but works well.

I'm confident this is a significant figures issue. Increase the number of significant figures in settings.

Thanks Jenny. I'm not a huge fan of the SIR model for an IA. But this is probably because I have not seen many good ones. It is difficult. I'll have a think and maybe make a video.

@@MrFlynnIB Thank you so much for considering it! It will be extremely helpful:)

Hey. I think this is a good idea. Just keep it simple. Don't overcomplicate it and the maths should be fine for an SL student.

It does.