Can You Solve The Martini Glass Puzzle? A Simple Illusion That Fools Most People

Рет қаралды 241,190

29 күн бұрын

Just how full is your cocktail glass anyway? The answer will surprise you.
Poll
• Post
CueMath
• How full is your glass...
DataGenetics
datagenetics.com/blog/february...
Subscribe: kzfaq.info...
Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas!
If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.
If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.
Book ratings are from January 2023.
My Books (worldwide links)
mindyourdecisions.com/blog/my...
My Books (US links)
Mind Your Decisions: Five Book Compilation
amzn.to/2pbJ4wR
A collection of 5 books:
"The Joy of Game Theory" rated 4.3/5 stars on 290 reviews
amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.1/5 stars on 33 reviews
amzn.to/1o3FaAg
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 54 reviews
amzn.to/1LOCI4U
"The Best Mental Math Tricks" rated 4.3/5 stars on 116 reviews
amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" rated 4.4/5 stars on 37 reviews
amzn.to/XRm7M4
Mind Your Puzzles: Collection Of Volumes 1 To 3
amzn.to/2mMdrJr
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 112 reviews
amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.2/5 stars on 33 reviews
amzn.to/1NKbyCs
"Math Puzzles Volume 3" rated 4.2/5 stars on 29 reviews
amzn.to/1NKbGlp
2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.
My Blog
mindyourdecisions.com/blog/
Twitter
/ preshtalwalkar
Instagram
/ preshtalwalkar
Merch
teespring.com/stores/mind-you...
Patreon
/ mindyourdecisions
Press
mindyourdecisions.com/blog/press

Пікірлер: 838

@webbraham2768 26 күн бұрын

I am half way through the video and forgot about the third dimension

@nemoyatpeace 26 күн бұрын

Yep, me too.

@randomname9291 26 күн бұрын

That was my exact mistake

@aba_dab_o 26 күн бұрын

Same. 😅 Was thinking between 70% and 80%, but closer to 70%.

@JonnyBoi957 26 күн бұрын

Yea I guessed that is what most people though. That is why I guessed 80% as it was a cone.

@jonothanthrace1530 26 күн бұрын

But first, we need to talk about parallel universes.

@trimeta 26 күн бұрын

Part of why so many people's intuition was 70% is that in the 2D case, the answer would be 1/sqrt(2), which is 70.7%. And although the wording was very clear that we're interested in the 3D case, the pictures themselves are naturally 2D, which colors our intuition.

@yfxxiii 26 күн бұрын

Yeah, my brain was doing maths with triangles because that was the visual I was presented with, instead of cones. It's another fun way to think about how easy to the mind is to trick (and often does the tricking itself).

@StRanGerManY 26 күн бұрын

Pictures are not naturally 2d. They are artificially 2d to mislead and confuse.

@trimeta 26 күн бұрын

@@StRanGerManY What's the shape of the screen you're viewing this on?

@talkingbirb2808 26 күн бұрын

@@trimeta you don't know how to draw a cone on a piece of paper? edit: I took a closer look and it's drawn like a 3D cone

@trimeta 26 күн бұрын

@@talkingbirb2808 Without doing a full-on animation (which arguably does add a third dimension -- time), it's hard to draw a cone that doesn't look like a triangle.

@47shawty12 26 күн бұрын

as a previous bartender, i knew it was 80% instantly. if you were to pour it into a glass of the same volume but with a cylindrical shape, it would be at the halfway mark.

@spacewolfjr 26 күн бұрын

another round, please

@CollegeHustler 26 күн бұрын

I was going to say the same thing! lol Real world experience is priceless!

@user-sl7ie9te5r 26 күн бұрын

@@spacewolfjr another martini, Paul?

@abhishankpaul 26 күн бұрын

What if a mathematician shows up there?

@phoquenahol7245 24 күн бұрын

@@abhishankpaul 2^(-1/3)

@deemjeffrey 26 күн бұрын

I guessed 80% bc i’m a bartender. Literally no calculation, just from working with martinis. Then you started proving it with math and I got so confused haha. Love your content. Thanks for everything!

@AiNaKa 25 күн бұрын

i'm not a bartender and i didn't calculate it but still guessed it right, i just figured it was common sense given the understanding that thinner volumes hold less fluid than wider volumes. martinis are cone shaped, so i figured they'd exaggerate the effect quite a bit, so my initial guess was 80%

@LONKULADE 25 күн бұрын

@@AiNaKa yea that's what I thought

@Zinozad 23 күн бұрын

I guessed 80% because it looked like that was the closest to half full. Not a bartender or anything.

@colinjava8447 22 күн бұрын

Technically 100/2^(1/3)% = 79.37% The angle doesn't matter cause stretching the glass horizontally and depth-wise will preserve the proportions.

@Zeptonixmusic 17 күн бұрын

I think that 80% of the height = 50% of the volume is not as mindblowing as 20% of the height being 0.8% of the volume

@paulgreen9059 27 күн бұрын

Without using a calculator I realized the answer was the cube root of one half. Then I needed a calculator.

@chrisglosser7318 27 күн бұрын

I had it memorized from when I used to to teach physics

@thomasdalton1508 27 күн бұрын

I approximately cubed 1.2 and 1.3 (I figured working with the reciprocals was easier - that may or may not have been true) in my head, realised it had to be somewhere between them and guessed 1.25, which corresponds to 80% so went with that.

@ThatFoxxoLeo 26 күн бұрын

Given the initial question was multi-choice, you could've worked backwards from there. 80% is 4/5, so you can just multiply 4/5 by itself twice to get its cube (4/5, 16/25, 64/125). 64/125 is very close to 1/2.

@christopherwellman2364 26 күн бұрын

@@ThatFoxxoLeoI like that explanation. Thank you.

@Dreamprism 26 күн бұрын

512 is 8^3, so .512 is .8^3, so .8 is close to cbrt(.5)

@zinaidalogunova5731 28 күн бұрын

Cone is really good shape of glasses for bars’ owners😀

@gregoryt1139 26 күн бұрын

And cubes. Don't forget cubes...Ice cubes. Plenty, plenty ice cubes.

@no_mnom 26 күн бұрын

If they don't fill it to the top, it's a sham!

@_xano 26 күн бұрын

„Con” is literally in the cone name so

@piershanson1784 26 күн бұрын

One thing about eyballing it is that when doing the poll with just eyballing it, I am naturally inclined to pick the triangle where the orange area is half of the volume rather than remembering that the triangle represents a cone which is what we're actually supposed to eyeball. When I eyball the triangle, 70% is definitely closer to half the area of a triangle, but since the triangle is supposed to be a cone, he 80% actually wins out.

@wmpowell8 27 күн бұрын

There's an intuitive explanation for the % volume = (% height)^3 formula: as the glass is filled, the shape that the water makes is scaled larger and larger with the tip of the cone anchored in place. Since a cone is three-dimensional, the volume of the cone is scaled in accordance with the cube of the scale factor of the lengths, thus, % volume = (% height)^3.

@martianunlimited 26 күн бұрын

I just used pretty much that, r is proportional to h , let's call r = ah, so rewriting that we have V = 1/3 a^2 h^3 since a is a constant, for V' to be 1/2 V, h' would just be 1/2^(1/3) h; it feels like we are just overthinking the problem.

@stuchly1 26 күн бұрын

@@martianunlimitedbut both of you are doing calculations 😂

@neuralwarp 27 күн бұрын

All the glasses are 100% full. It's just a matter of what they're full of.

@user-pr6ed3ri2k 26 күн бұрын

my glass is filled with 90% water and 10% bose-einstein condensate

@Ejemplo-lz8ql 26 күн бұрын

"It's just a MATTER of what they're full of" Pun intended?

@fatmccat1513 26 күн бұрын

@@user-pr6ed3ri2k Mine has 10% quantum foam

@user-pr6ed3ri2k 26 күн бұрын

@@fatmccat1513 what's the other 90%

@Bleaksigilkeep 25 күн бұрын

As a former bartender I do have to make a minor correction in that a Martini glass actually should be filled to nearly the rim. The purpose of the glass is to give the volatile aromatic molecules a large surface area to evaporate into the air but not to enclose and capture them, so that when sipping you get a strong aroma from the drink only at the moment you first bring it to your face to sip, not throughout the motion of tipping the glass to drink. The glass should be filled almost completely to the rim, like 95%. Even 80 or 90 will give too much room for the aromas to collect and the intended effect of the first sip will be list, as the drinks nose will be full of hot alcohols and terpenes

@Inspirator_AG112 27 күн бұрын

*Remember that the real-life counterpart of that diagram is 3-dimensional...*

@Nukestarmaster 26 күн бұрын

Yeah, that was what got me, lol. 2d diagrams are a nasty trick.

@Clyntax 22 күн бұрын

A much simpler way to approach this is to observe that both cones are similar. So you want to scale down the larger cone in order to half its volume. Scaling a body does not depend on the shape at all, it can even be done with a cube. If you scale a body in 3D by factor s in every dimension, the volume increases by a factor of s^3. We want to know the scale factor x so that the volume factor is one half: 0.5 = s^3. Therefore, x = 0.5^(1/3) which is almost 0.8 and the answer to the question. No pi, radius, graphs or complicated formulas needed.

@andredavis4657 9 күн бұрын

That's the way I did it

@1104Tea 26 күн бұрын

Its easy to assume wrong when you're presented with a 2-d image for the options, in a question that wants an answer based on 3 dimensions. What everyone learns in school is to go with what information is presented if the problem doesn't specify any detail. I know some people will try to be cheeky and say they top of the drawing may imply something, but we all know that can just be there as an artists choice for making any generic 2d cup.

@Tomyb15 26 күн бұрын

Yeah, I didn't think about the diagrams enough and made a simple mental calculation based on 2D cups and got 70%, but in 3D it gives 80%.

@senbatifanola 26 күн бұрын

Ah yes a 2D glass

@Questerer 26 күн бұрын

I’ve never heard of a 2D liquid. The question implies that it is in 3D.

@Misteribel 26 күн бұрын

I'd love you to pour me a 2d drink! How many ml go into a 2d martini glass? 😂

@SuperClavera 26 күн бұрын

@@Questerer When 60% assumes something "wrong" based on how the question is presented, then there's absolutely something wrong with the question, especially since their answer is correct when calculating the area in 2D.

@rorywquin 26 күн бұрын

I knew the answer immediately. I came across this in the early 1980s. I was in a bar (in a place called Klerksdorp in South Africa) when two people ordered liqueurs. One wanted a single and the other wanted a double. The barmaid poured their drinks (by eye) into the same size glass. The guy with the double complained because he felt the guy with the single was getting a better deal (more than a single). She got a tot measure & poured a single into it and topped the glass (with the single) up. It came to exactly the same level as the double (she was pretty good at her job).

@MrMousley 16 күн бұрын

Exactly the same thing happend to me when I worked behind a bar, A 'double' served in a proper martini glass is NOT 'twice the height of liquid in the glass'. That's why I always used a measure and poured the drink into the glass in front of the customer.

@maxc300s 26 күн бұрын

People that clicked 70 percent because they thought of the martini as 2d and not 3d here 👇👇👇👇👇👇

@annoyingbstard9407 18 күн бұрын

Did you really do that? 😂

@jwdory 11 сағат бұрын

I never heard of a 2d martini. What are you a flat lander?😅

@SteinGauslaaStrindhaug 25 күн бұрын

1:20 Assuming the inside is not a truncated cone, i.e. it's pointy all the way down, the angle should not matter. My intuition says it's around 75%, but it wouldn't surprise me if it's closer to 80%.

@justdilka 27 күн бұрын

I'm a martini glass half full kinda person

@Minetendo_Fan 26 күн бұрын

So are you 1/8 full or 80% full?`

@Matty0311MMS 26 күн бұрын

Maybe @justdilka is in a quantum superposition of both?

@chobies5383 23 күн бұрын

I'm a " Martini to the half way point"

@suntzupup 27 күн бұрын

I knew it was 80. Didn't calculate it but I could feel it when I pour and it had pissed me off for years.

@Dexaan 27 күн бұрын

This is why there's usually something like (20 cl) next to the wine descriptions in restaurants. Mixed drinks are usually sold by the shot, as well.

@kylejacobs1247 27 күн бұрын

The misleading part of this question is that it is presented as a 2D problem visually, when in fact it is a 3D problem.

@harry2.01 27 күн бұрын

I fell into the same trap.

@MrJoerT 26 күн бұрын

In 2d 80% is still the closest answer, right?

@lidarman2 26 күн бұрын

@@MrJoerT I think it is 70.7% for 2d case. Solve the 2d version, 1/2 = x^2.

@c.jishnu378 26 күн бұрын

Underrated.

@drenz1523 26 күн бұрын

Visually 2d? There's an oval at the top, an oval at the bottom, glasses irl are clearly 3 dimensional, 2d glasses don't exist (closest you'll get is a very flat prism glass), etc

@ThePowerfulOne07 27 күн бұрын

That explains why my iPhone thinks 80% battery level is considered full!!!

@Temporary_yesyes 27 күн бұрын

it only goes to 80% to preserve battery life overall

@ThePowerfulOne07 27 күн бұрын

@@Temporary_yesyes trust I know and for full performance and capacity as well!

@amanavinash-fb4zk 26 күн бұрын

this video explains the opposite

@chriswebster24 26 күн бұрын

If the height of the liquid is 80%, the glass would only be about half full. If the glass is 80% full, the height of the liquid would be about 93%.

@sunrevolver 26 күн бұрын

Rofl

@bootlegharold6696 26 күн бұрын

Presh that was needlessly overcomplicated lol

@kyyzh12 27 күн бұрын

I remember me and my dad figuring out where you would have to cut a cone into 2 perfect pieces. We also got ~79.4%

@noomade 26 күн бұрын

surely you cut the cone vertically down the middle....

@kyyzh12 25 күн бұрын

@@noomade lol this is what we thought when seperating a cone into 3 equal pieces

@chimingchan9038 26 күн бұрын

Very nice analysis👍👍

@doctorb9264 26 күн бұрын

Excellent problem and solution.

@StephanBuchin 26 күн бұрын

I'm even more impressed by the fact that the 50% height is only 12.5% full.

@lefthanded3512 27 күн бұрын

Wow, surface area really makes a difference

@frumbert 26 күн бұрын

INtuitively I said 80%, since the volume goes up the wider the glass. Nice to see it explained.

@Dejiek0 26 күн бұрын

Very interesting. I solved this with integration using similar triangles before I saw your elegant solution.

@sugurlu1 26 күн бұрын

Great video, thank you.

@markfoxwell2411 26 күн бұрын

A good reason for using calibrated shot measures.

@williamlennie 26 күн бұрын

Solving this problem is way more fun with trig!

@KiranRajagopalanMusic 25 күн бұрын

Cuemath is doing a wonderful job, thanks for calling it out 💪

@ShotgunLlama 27 күн бұрын

Now hol up. Who said it has to be a cone? What if we're looking at a cross-section of a triangular prism?

@deathpacito8702 27 күн бұрын

The math works out to be the same, since volume still scales with height^3 EDIT: NVM, mixed up prism and pyramid. If it's a triangular prism then yeah 70% should be the answer here.

@duanecjohnson 27 күн бұрын

Doesn't make a difference. Any prism is 1/3 cubed route of height. A cone is just a many-sided prism. AD0TJ

@geraldsmith6225 26 күн бұрын

Than it wouldn't be a martin glass

@protoman1365 26 күн бұрын

@@deathpacito8702the volume of a rectangular prism is triangular area (which is the cross section we see) * the length of the glass in the Z axis. Since the length of the glass at any given moment is unchanged, wouldn’t the answer change to 70%, as only two dimensions change instead of three and it’s related to the square of the height instead of the cube?

@deathpacito8702 26 күн бұрын

@@protoman1365 Ah my b, mixed up prism and pyramid

@rogue5882 26 күн бұрын

Without having to rearrange, the volume scale factor for a 3d object is (the length scale factor) ^3

@MorgurEdits 26 күн бұрын

If you have one of those measuring containers with similar shape you can notice how often the value changes at the top and how rarely it changes on the bottom, that is why I was one of the 23%

@umchoyka 26 күн бұрын

80% - I had a good intuition on this. As someone who makes a pot of pour over coffee every single morning in a cone filter, I have a very keen awareness of when the pot is almost done brewing.

@Peter_1986 26 күн бұрын

I used the disk method from calculus for this problem, and found the distance from the origin at where I would get half of the full volume of a cone.

@lidarman2 27 күн бұрын

I knew the answer because I recalled doing a similar thing in 1st semester calculus 40 years ago. I think we had to calculate the rate of volume change vs height of liquid change. I also thought of the pizza size vs diameter optimization here and knew since it was 3d, it would be a cubic instead of a square.

@feynthefallen 19 күн бұрын

I saw this demonstrated in tv education program back when I was a child. They did it for several shapes and demonstrated the relation of shape to certain graph shapes. Taught me more about mathematics than any two of my school teachers.

@henk-ottolimburg7947 26 күн бұрын

You don't need the formula of a cone, for many very difficult with pi etc. The glass can be any form It's enough if the partly filled glass is an image of the full glass. The factor is 0.6 or 0.7 and it works in 3 dimension to the 3rd power. 0.8 * 0.8 * 0.8 is approx 0.5

@alopexlagopus1488 26 күн бұрын

As soon as percentages were introduced without the x100 factor when one side of the equation was cubed, it makes the equation out by a factor of x10000. Very surprised at Presh for incorrectly converting to percentages rather than sticking with ratios.

@hippophile 26 күн бұрын

70% makes sense for our eyes because we intuitively see 70% as half the glass, looking at it we see a 2-dimensional picture - and indeed, the area of the smaller triangle at 70% height is 49%, because it is a square relationship. Cubic relationship is more extreme, so 80% feels right...

@jean-francoisbouzereau6258 26 күн бұрын

In the graph, the axes must only be oriented toward the positive direction only.

@deezillusioned9909 26 күн бұрын

If you work with a measuring cup a lot, you would kinda have an idea to what height it might be, i know its not the same shape but the similar concept.

@oneeyejack2 26 күн бұрын

If two 3D objects are similar, the ratio of the volumes is always the ratio of lengths cubed

@Maxime-fo8iv 26 күн бұрын

I usually solve your riddles from the miniature, then I just skip to the answer and like. Not sure if that helps the algorithm, but in any case thank you very much for all those riddles!

@Nfscarbon07 26 күн бұрын

YES I figured 80% because of videos I've seen about shot glasses showing how much alcohol you can lose out on, 70 was my first guess but it seemed low to me

@mordechaisnyder7808 26 күн бұрын

Whew! Glad to be in the 28% that selected 80%! When I saw the results leaning so heavily to 70%, I assumed I’d totally botched it. Great puzzle Presh!

@wintersxlstice21 26 күн бұрын

i’ll keep this in mind for my bladder

@youssefelyousfi4929 26 күн бұрын

great puzzle

@X22GJP 26 күн бұрын

My intuition was correct - just looked right; but then I immediately thought in terms of volume.

@musanim 8 күн бұрын

Or to put it another way: the liquid in the glass is a 3-dimensional volume in which the x, y, and z sizes (height, width, depth) all vary proportionally together. Volume is x*y*z, so, the answer is the cube root of one half.

@r.markclayton4821 26 күн бұрын

@MicMan123456789 26 күн бұрын

80% seemed right to me just because the area of the crossections increase by a squared factor

@dogberry20 26 күн бұрын

I didn't do calculations, but I did think of it as a triangle, and then visually cut it in half and made it into a rectangle. It didn't give me the correctvolume, but it gave me the closest answer.

@musicxnr8876 26 күн бұрын

my intuition worked wow

@gaijininja 26 күн бұрын

Damn, I was one of the small percentage that guessed 90% on the earlier poll. I thought it would be similar to the question about lily pads covering a lake by doubling each day. (That one is 1/2 covered on the second to last day.)

@duanecjohnson 27 күн бұрын

A cone is a special form of a pyramid. Which is also the cubed route of base * height. AD0TJ

@RR-vk2tl 26 күн бұрын

That is the reason why they use this shape of glass in the bars

@luketurner314 19 күн бұрын

Had a head start thanks to Numberphile's video yesterday on the exact same problem. One could construct an Euler diagram of the audience/viewers/subscribers of this channel and that one

@Lost_City007 26 күн бұрын

8:03 @MindYourDecisions He said " v/V = % of the volume of the large cone ". No, it is only the percentage like ( y %). Value with %... So the relation is y % = (x %)³

@yousifshtifa7684 19 күн бұрын

Amazing work, can I know what software you are using for such a beautiful presentation as well as mathematical and graphical illustrations? Thanks.

@Matthew.Sweeney 19 күн бұрын

very sneaky to make it look like a poll about area when it's really a poll about volume

@Altoclarinets 26 күн бұрын

I sat down and mathed this out for the fun of it, but if you asked me this question at a party, I would just get a book (or other hard, flat object), firmly cover the end of the glass, and turn it horizontal to see which one had a liquid level that reached the point of the cone. This is called solving by brute force, and while it's not mathematically efficient when there are many examples to be tested, for a set as small as this (particularly considering that I had already eyeballed the 80% one as looking right so probably would have began there) it is good for making your point quite aggressively

@MushookieMan 27 күн бұрын

New bar trick unlocked

@Matty0311MMS 26 күн бұрын

I answered this intuitively, and calculated it later by cubing the decimal values of the percentages. I picked 80%.

@pramodsingh7569 27 күн бұрын

Thanks

@programmerpctheory1413 25 күн бұрын

Next time you want a shortcut to use for any general shape, just use the square cube law. or in this case the line cube law (I think I made it up).

@mattjanzen2344 26 күн бұрын

Bartender here. Drink recipes are measured independent of the glass. Then you consider "wash lines" - the point at which a given glass is visually "full", while still allowing it to be carried comfortably without spilling. With final volume of the drink and volumes of various glasses at their wash lines all known, an appropriate glass can be selected - or recipe and price adjusted.

@castleanthrax1833 27 күн бұрын

The number of comments (on the poll. Not this video) who were saying that it depends on whether the glass is 3d or 2d, astounded me. How anyone could fill a 2d glass with liquid is beyond my understanding.

@mofprailes7140 27 күн бұрын

Can work tho with 2d drawing animation I guess

@castleanthrax1833 27 күн бұрын

@@mofprailes7140 The question was clear. It said LIQUID.

@Songfugel 27 күн бұрын

Because they forgot what the problem was, since the graphic is 2D with a very hard to see 3D glass rim, especially on mobile. It is pretty easy mistake to make if not paying attention

@GooogleGoglee 27 күн бұрын

In 2 dimensions I can color the surface of the glass with a marker.... That is liquid. But hey 😂 I am joking here 😉

@Idiomatick 27 күн бұрын

My guess was based on 2d as well... i just saw it as a triangle

@ericwickeywoodworkersurfbo6135 26 күн бұрын

That was killer.

@BeyondKawaii 26 күн бұрын

What I did first is taking the formula of the volume and substituted r with its expression through h and the angle. Now that h became the only variable - I solved for the ratio of h, which would half the volume.

@first_namelast_name4923 23 күн бұрын

I did the calculation, but not because I wanted to cheat, but I enjoy doing calculations - and this is the reason I like this channel. I did the calculation to see whether my guesstimate was right, before I un-pause your video, just like I usually do with your videos ;-)

@drelijahmikail3916 26 күн бұрын

we can `sense` the intuition with the volume formula: V = pi*r^2*h/3, that the r is a power of 2 with delta{h}. Therein, delta{h} in increment of %, can lead to a power of 2 increase.

@JLvatron 26 күн бұрын

Math for Alcoholics! lol!

@jensraab2902 26 күн бұрын

Hey, if that's what it takes to make people interested in math, so be it! You know those people who whine about math, saying "when will I ever need this in real life?" Well, here's an example!

@gorak9000 26 күн бұрын

iDz tHe BezZt kInDuh mAtHhHhHhs

@JLvatron 26 күн бұрын

TeeHee-ous replies!

@FosukeLordOfError 26 күн бұрын

7:57 I need more math in my life I was so close to this before I watched this part. Getting the ratio of volumes was the part I missed because I was trying to solve a specific case instead of the general.

@rvsingh56 20 күн бұрын

I remember seeing a video somewhere, discussing the volume of a cone. I am also a math student so I instantly guessed it was 80% without calculation, as the lower part would contain lesser volume of the drink. Most of the volume of the glass lies in the frustum of the cone.

@TakeruDavis 26 күн бұрын

Based on the crossection of the glass being a triangle, I instinctively thoughts something around 75% and considering the 3rd dimension, I hedged my bet on 80%

@nzeches 26 күн бұрын

Height is proportional to the radius, so volume is proportional to the cube of height. Hence 1/2=v2/v1 = (h2/h1)^3

@lordsmeagol3390 25 күн бұрын

I immediately concluded: volume of cone => 1/3 base area times height; Base area is proportional to the square of the height => volume proportional to height cubed => for 1/2 volume, height is cube root of 1/2

@shruggzdastr8-facedclown 24 күн бұрын

This feels related to the cube-square law, which demonstrates that there is a lag between how much the surface-area of a given solid increases when you double its volume. Said surface-area only increases by the square of the cube-rt of 2 (e.g.: 2^(2/3)). Conversely, when you double the given solid's surface-area, you more than double its volume

@jackmclane1826 26 күн бұрын

Given the strength of a well made Martini, the small volume is a good thing.

@TheMofRider2 26 күн бұрын

When I saw the thumbnail I did the calculations in my head, then wondered why I managed to cancel out the relation to the angle, so I watched your video where you made the exactly same calculations and still can't picture (but I understand the maths behind) how this can not depend on the angle...

@AFSMG 26 күн бұрын

How wonderful, I will keep that in mind every time they give me a glass of wine.

@btfofffice 9 күн бұрын

Draw a line down the middle. Square it and then measure the Area of the two squares

@Bavarianscience 26 күн бұрын

There's actually a shorter way to do the calculation. The cross sectional area of the cone shaped glass is equal to pi*r^2. r is directly proportional to the hight because it's a cone so the area has to be directly proportional to the hight squared. Then we can simply integrate this h^2 term with respect to the h and we get the volume to be directly proportional to 1/3*h^3. The factor of 1/3 can be ignored like any other constant factors thus far. That way it becomes clear that the answer has to be close to the cube root of 1/2 which is 79,37% or nearly 80%.

@a.n.x.i.e.t.2761 26 күн бұрын

Fascinating

@AFSMG 26 күн бұрын

Excelente ejercicio. Extraordinario

@djwarner7144 26 күн бұрын

High school geometry says the area of similar figures vary with the square of the ratio of linear dimensions. Similarly, the volume of similar solid figures vary with the cube of the ratio of linear dimensions.

@user-ql9oz8wu7t 27 күн бұрын

I had my insight due to a jigger measure. 1 1/2 oz was almost full on a 2oz measure.

@MaraFaris 27 күн бұрын

Yay! I guessed it right! So I tried to visualize an imaginary line on the two dimensional glass extending from the top-right corner to the middle of the left leg of the triangle, cutting it into two even right triangles (And thus create a visual for what 50% full would look like from a different perspective). Then I sorta imagined tipping each of the pictured glasses until the liquid was at the top right edge, just before spilling out. Then I just tried to visualize which of the options put the water level at that 50% point on the left leg of the glass, and the 70% image felt like it would come up too low, but the 80 landed just right.

@ericblase4873 14 күн бұрын

I only guessed 80% because my wife and I did a test to measure our jiggers in ounces for cocktails and it was crazy how much more volume a full jigger was to a close to full one. Jiggers weren’t cones but led my intuition for this problem.

@GroovingPict 25 күн бұрын

you say it's completely counterintuitive, but I not only got the correct answer, but also figured it was slightly overshooting (ie that the 80% height was slightly more than 50% volume) which was also correct. No calculation (I wouldnt know how to do that anyway), just intuition

@thegreatgreenarkleseizure1994 26 күн бұрын

I did the math 'wrong' in that, in my head, I knew the volume was 1/3*area*height, and I just thought that I would multiply that by 1/2 being the 50% height mark, but intuitively the halves aren't 'equal' like they would be in a cylinder, but more volume in the widest (upper half). Thus roughly 1/6 (1/3*1/2) of the 'fat' side of the cone height is where the 50% should be and that is about 17%, thus 83% 'full' is halfway there going from the other direction. Not correct, but a close estimate without dealing with roots and whatnot. Glad you pointed out my error (and I always love this stuff because I've been out of school for decades).

@vbinsider 20 күн бұрын

The only thing I knew for sure right at the beginning was that the answer does neither depend on the angle nor on the volume of the glass. It's basically the same result as for why the water pressure does not depend on the area of the sea in which you are diving but only on the diving depth.

@johnrains8409 12 күн бұрын

Before anyone asks, whether a glass is half full or half empty (assuming it has liquud up to the halfway point) depends on the sign of derivative of the level with respect to time, dL/dt. To determine this, you must know the level just prior to it reaching the halfway point. If this is deri ati e is negative, the level is going down and it is half empty. If it is positive, the level is rising and the glass is half full.

@rajehhuawei1588 21 күн бұрын

You could use a similitude. The two cones are similar to each other. The ratio of volume is the cube of the ratio of height(in 2d the ratio of area is the square of ratio 10:02 ). So( r1/r2) ^3=v1/v2. And we get ,for sure,same result.