The Napkin Ring Problem

Brain Candy Live FALL TOUR:
The Curiosity Box:
my twitter: tweetsauce
Adam and I (but mainly Adam) making a kendama:
Orange Oil:
Napkin Ring Problem:
Cavalieri's Principle:
Eric Langlay stayed up all night with me so that this video could come out today. MUCH LOVE
Grant from 3Blue1Brown helped me wrap my head around this topic:
music by
Jake Chudnow:
and via AudioNetwork:


  1. Vsauce


    3 jaar geleden

    Sorry Napkinheads, but the solid shown from 0:18 to 0:24 is not a proper mathematical "napkin ring." It shouldn't have flat faces on the top and bottom. That's a mistake I missed in my rush to export this episode before my flight to Montreal this morning :( But I'm glad to be in Montreal! I'm here working on an episode about the power of suggestion ...

    • TheJohnMan


      7 dagen geleden

      500 comment

    • Cartoon Chaos

      Cartoon Chaos

      11 dagen geleden


    • Mitzi Brabb

      Mitzi Brabb

      Maand geleden


    • Mitzi Brabb

      Mitzi Brabb

      Maand geleden


    • Ashwin’s Magic And Cardistry

      Ashwin’s Magic And Cardistry

      2 maanden geleden

      Last comment

  2. D'Nicky Karito

    D'Nicky Karito

    16 uur geleden

    Am I the only one whose brain hurts?... Yeah?... Ok

  3. Green Cheek Beak

    Green Cheek Beak

    Dag geleden

    2 good at math for me

  4. Atlas Hellwalker

    Atlas Hellwalker

    2 dagen geleden

    Yo, this is kinda mind blowing.

  5. Pearl Kids

    Pearl Kids

    2 dagen geleden

    “yay, *with teeth* “ why is that so damn funny oh my god- (8:43)

  6. thenewbgamer64


    2 dagen geleden

    My mom learning of this: very interesting. My mom when I explain how water isn't wasted, as non has left the earth not entered: what are you learning?

  7. Yeet 51

    Yeet 51

    2 dagen geleden

    Thumbnail looks like Opera browser logo as seen from the bottom

  8. _-Voxeliorn-_


    3 dagen geleden


  9. Pekka Laitinen

    Pekka Laitinen

    3 dagen geleden

    0:50 me when somebody informs me there's a spider on my shoulder

  10. GeneralOfShadow


    4 dagen geleden

    Today I learned that Orange Oil can burn.

  11. Darius Foster

    Darius Foster

    5 dagen geleden

    0:51 Pause

  12. マハア


    6 dagen geleden

    Thumbnail: Opera browser

  13. Sam Kroon

    Sam Kroon

    6 dagen geleden

    That's math

  14. Chris Garcia

    Chris Garcia

    6 dagen geleden

    The eclipse he’s talking about happened the beginning of my senior year of HS I’m 21 now. Simpler times...

  15. dovahkiin777s


    6 dagen geleden

    That hurt the math muscles I didn’t know I had

  16. Tosty


    7 dagen geleden

    Does that also mean that if I cut a napkin ring out of the earth with the height of an orange, that this napkin ring has teh same volume as said uncut orange?

  17. Angus Fraser

    Angus Fraser

    7 dagen geleden

    Napkin Rings look like Napkin Rings.

  18. TheJohnMan


    7 dagen geleden

    Me watching sauce for memes but actually try to listen I like your funny words magic man

  19. Kuuke


    7 dagen geleden

    What if the larger napkin ring has a smaller inner circle, thus giving it more area?

    • Punit Meena

      Punit Meena

      5 dagen geleden

      @Релёкс84 ohh i get it now , can't believe i missed that

    • Релёкс84


      5 dagen geleden

      If you make a smaller circle, it will make the napkin taller. The fixed height of the napkin uniquely decides the radius of the cylinder you carve out.

    • Punit Meena

      Punit Meena

      5 dagen geleden

      oh wait yeah how are they deciding what should be radius of the cylinder for the napkin ring

  20. Orange Juice

    Orange Juice

    7 dagen geleden

    That's doesnt sound right but....

  21. Danielle


    8 dagen geleden

    Okay but why are we subtracting the area of the cylinder cross section from the area of the sphere cross section in the first place?

  22. MrWestonO


    8 dagen geleden

    Why do i see the opera logo

  23. Sakkara N

    Sakkara N

    8 dagen geleden

    that's sick

  24. moon key

    moon key

    8 dagen geleden

    Ok, wait. You say that any two rings of the same height will have the same volume? What about if i had two oranges exactly the same size. Took out a 1 cm core from the first one, and a 10 cm core from the second one. The remaining "napkin rings" are going to have different volumes. Right? Am i not getting something?

  25. AlphaK


    8 dagen geleden


  26. Winkler


    9 dagen geleden

    "By the way, Orange oil is flammable." - Michael from Vsauce "You're the best, Michael." - Me

  27. Oliver Goat

    Oliver Goat

    9 dagen geleden


  28. joseph


    9 dagen geleden

    Never look at napkin rings the same again

  29. Derek Townsley

    Derek Townsley

    9 dagen geleden

    Was this video reposted, I thought it was newer until i heard him talk about August 21, 2017 as a future event lol

  30. Michael Villarreal

    Michael Villarreal

    10 dagen geleden

    I love that we share the same name, keep going vsauce your videos are amazing

  31. Gil Gordon

    Gil Gordon

    10 dagen geleden

    if you take a sphere the size of the earth and take out a hole the thinness of a pin from the earth sized sphere and take an apple and take the core out, would those "napkin rings" really be the same. I don't believe it.

  32. Bigmike.v1


    11 dagen geleden

    What does high school algebra do for me? Well, it helps me understand half of this video

  33. Jesus Freak

    Jesus Freak

    11 dagen geleden

    "By the way, orange oil is flammable." Okay let's move on.

  34. Joe Guy

    Joe Guy

    13 dagen geleden

    It was my birthday when the eclipse happened :)

  35. Zaiden Patton

    Zaiden Patton

    13 dagen geleden

    But u could fit more in something bigger

  36. Easton Kimbrough

    Easton Kimbrough

    13 dagen geleden

    By the way orange oil is flammable

  37. Alex Maniatakes

    Alex Maniatakes

    14 dagen geleden

    You're a mage eh

  38. peppuhroni


    14 dagen geleden


  39. GameBOI


    14 dagen geleden

    I feel like “orange oil is flammable” is going to be important in some obscure future event in my life

  40. Irmonch


    14 dagen geleden

    3:07 find the differences between these two pictures Vsauce: they're the same picture

  41. Victor F.V

    Victor F.V

    14 dagen geleden

    I was scared he was going to use triple integrals and spherical coordinates to determine the volume of the napkin rings.

  42. daniperez


    15 dagen geleden

    0:18 is not a good animation because it shows a flat face on both top and bottom surfaces which makes the theory invalid.

  43. Tacoman


    15 dagen geleden

    From 3:10 to 8:44 my brain melted

  44. Matt Roig

    Matt Roig

    15 dagen geleden

    Thought Micheal was going to tell me something about the Opera browser

  45. Matthew


    15 dagen geleden

    3:42 fu*k u vsauce mikael

  46. Mark Meyer

    Mark Meyer

    15 dagen geleden

    The people who disliked the video dont use a napkin after eating ribs

  47. James Ellison

    James Ellison

    16 dagen geleden

    watching michael do math is relaxing

  48. Cutwitha Knife

    Cutwitha Knife

    16 dagen geleden

    Hey I like your shirt

  49. Static Rain

    Static Rain

    16 dagen geleden

    "Yay, with teeth" 👁️👃👁️ 8:42

  50. FoxToFreedom


    16 dagen geleden

    I just like how he occasionally adds it: oh yeah and orange oil is flammable

  51. Jerald Allen

    Jerald Allen

    17 dagen geleden

    What the hell did I just watch Micheal do 😂 0:48

  52. Diamondbac


    17 dagen geleden

    Wouldn't the diameter of the core matter? How much should be cored out from both spheres for this law to work? Or is there a definition to coring that I'm missing?

  53. kelly hill

    kelly hill

    17 dagen geleden

    And I was told in high school that I would need that stuff later in life....and I didn't believe them. Boy was I wrong little did I know that one day there would be this thing called the internet ,and on this new technology there would be another thing called youtube and on this thing there would be a guy measuring the area of a napkin holder ,AND BAM !!!! the importance of knowing that stuff that they tried in vain to teach me.

  54. kelly hill

    kelly hill

    17 dagen geleden

    You lost me on napkin holder

  55. Angel Rocha

    Angel Rocha

    17 dagen geleden

    0:49 me after I did a line.

  56. mrloleno


    17 dagen geleden

    My napkin at night: of course i know him, its me

  57. YJArts


    18 dagen geleden

    falling asleep to this fes like falling asleep during class lol

  58. Kylynn Boi

    Kylynn Boi

    18 dagen geleden

    John 15:18-22 NIV “If the world hates you, keep in mind that it hated me first. If you belonged to the world, it would love you as its own. As it is, you do not belong to the world, but I have chosen you out of the world. That is why the world hates you. Remember what I told you: ‘A servant is not greater than his master.’ If they persecuted me, they will persecute you also. If they obeyed my teaching, they will obey yours also. They will treat you this way because of my name, for they do not know the one who sent me. If I had not come and spoken to them, they would not be guilty of sin; but now they have no excuse for their sin. If you just repent of your sins, and belive that Jesus died for YOU, you will go to heaven. You can only go to heaven through faith, not by works of the world, which means you can't do good things on earth and expect to go to heaven, you only go to heaven through faith.

    • Kylynn Boi

      Kylynn Boi

      17 dagen geleden

      @_ because I am a true believer in Christ and I want as many people to get to heaven as possible. I do this by spreading the gospel by commenting that comment I said on videos that I watch

    • _


      17 dagen geleden


  59. steticc ඞ

    steticc ඞ

    18 dagen geleden


  60. Strate Up Gamr

    Strate Up Gamr

    19 dagen geleden


  61. juancgutro


    19 dagen geleden

    "Yay... with teeth"

  62. Mohamed Chaabouni

    Mohamed Chaabouni

    19 dagen geleden

    Hoped my math and physics teacher was explaining like you. XD thanks !

  63. A person

    A person

    19 dagen geleden

    I dont understand but cool

  64. Ares Quinn

    Ares Quinn

    20 dagen geleden

    this is so wierd

  65. Jo Lopez

    Jo Lopez

    20 dagen geleden

    The most original way to ask my girlfriend if she wants to marry me!

  66. Cringowa Chan

    Cringowa Chan

    20 dagen geleden

    me who didn't have half of that crap on math yet: *yes, i understand e v e r y t h i n g/s*

  67. Sir Picklestien

    Sir Picklestien

    20 dagen geleden

    Everyone talking about napkin rings but what about 1:33 ...

  68. Sir Picklestien

    Sir Picklestien

    20 dagen geleden

    Really satisfying ASMR to play in background during tasks!!

  69. Moises


    20 dagen geleden

    Ah yes, math

  70. haynuzband


    20 dagen geleden

    how does square root work on one side and not the other at 5:20?

    • Rixasum


      19 dagen geleden

      so that you know that you need to sq root it when R and H are a number

  71. robbie rasberry

    robbie rasberry

    20 dagen geleden

    Daily Dose of Internet

  72. Ishaan gupta

    Ishaan gupta

    20 dagen geleden


  73. Himanshu Patil

    Himanshu Patil

    20 dagen geleden

    After 10min 44 sec: Sooo.... What is a napkin ring?

  74. helpmelah


    21 dag geleden

    I see *oracle*

  75. L O R D . R U N S A R K

    L O R D . R U N S A R K

    21 dag geleden

    This was a math lesson

  76. GMS Films

    GMS Films

    21 dag geleden

    I know no one uses the web browser oprea and neither do I but, the title card

  77. EarthToAccess


    21 dag geleden

    michael why is the thumbnail a sideways Opera logo /s

  78. clear cut

    clear cut

    21 dag geleden

    No homework for today folks We'll continue tomorrow with the same chapter. And as always, Thanks for watching

  79. Chizuru


    22 dagen geleden

    0:38 let's leave

  80. Mr_Pro_ 244

    Mr_Pro_ 244

    22 dagen geleden

    I can’t stop thinking about three-point hitches on tractors while watching this 😂

  81. Dennis Greenwood III

    Dennis Greenwood III

    22 dagen geleden


  82. GreenJordan 30

    GreenJordan 30

    23 dagen geleden

    Opera browser.

  83. 5Cents


    23 dagen geleden

    I remember seeing your brain candy back in the day, unfortunately I lost my ping pong ball 😢

  84. Mad Wolf Man

    Mad Wolf Man

    23 dagen geleden

    yay, with teeth

  85. Timothy McQueen

    Timothy McQueen

    23 dagen geleden

    Holy shit, do I hear Kira's theme from JoJos?!?!

  86. Lamar Davis

    Lamar Davis

    23 dagen geleden


  87. Jack Cable

    Jack Cable

    23 dagen geleden

    Fun fact! If you turned the earth into a napkin ring everyone would die

  88. John MacLean

    John MacLean

    23 dagen geleden


  89. Swaggerlol


    24 dagen geleden


  90. Patrick Vroman

    Patrick Vroman

    25 dagen geleden

    9:36 The view of the eclipse from "Organ" was amazing.

  91. Jacquelin Simpkins

    Jacquelin Simpkins

    25 dagen geleden

    0:50 Michael are you ok?

  92. Sage Royale

    Sage Royale

    25 dagen geleden

    I thought this vid was about opera

  93. DoYouRememberHim


    25 dagen geleden

    Me: wants to learn about napkin rings but gets an entire math lesson instead

  94. deano2000nz


    26 dagen geleden

    Sorry, but I'm off to watch some more porn

  95. Ajay Whitfield

    Ajay Whitfield

    26 dagen geleden

    I failed algebra 2 in high school.....I understand this Completely!!! Oil from Oranges are Flammable!!!!

  96. Bruno Reblin

    Bruno Reblin

    26 dagen geleden

    So we can make bombs out of oranges?

  97. Juan D'Marco

    Juan D'Marco

    26 dagen geleden

    Wow 😳

  98. UrBoiChipsAhoy


    26 dagen geleden


  99. Jay Mac

    Jay Mac

    26 dagen geleden

    How come you didn’t evaluate the definite integral that would have shown the volume of a napkin ring?

  100. Wisconsin Wintergreen

    Wisconsin Wintergreen

    26 dagen geleden

    *Looks at thumbnail* Get out of my head. Get out of my head. Get out of my head. Get out of my head. Get out of my head. Get out of my head. Get out of my head. Get out of my head. Get out of my head. Get out of my head. Get out of my head. Get out of my head.