Volume of a cone | Perimeter, area, and volume | Geometry | Khan Academy

[@variannevo642]

Thank you so much! This video actually helped me earn an A on my math quiz.

[@willywonka2615]

👍

[@footballworld3869]

This man his drawing is awsome!

[@masonwong895]

yes it is

[@astrq1un3]

y e s i t i s

[@MrMShake]

Please can you guys make a video to calculate the surface area using integration

[@Paradox_Incognito]

Thank you so much!!! I'm watching your videos over the summer to help remember what I learned this school year

[@dorinemorris4667]

This man's drawing is spectacular! :)

[@marcarias5350]

oh yes i learned so much!!!!!!!!!!!!

[@irlallan]

Bro actually explained a 45 min geometry course in 5 mins - like that's insane!

[@irlallan]

also who else is in 2023 rn?

[@TiberiusStorm]

I have a Texas Instruments calculator but I had to input it differently than Sal to get that answer. r = √393/(5π)

[@-MissSiri-]

I WANNA SING YOU HAPPY BIRTHDAY YOUR DRAWINGS AND TEACHING STYLE ARE AMAZING!! ❤️

[@PRINCE-he3wr]

Explanation for the cone’s volume to be 1/3 less than that of a cylinder Because, If you fill water in a cylinder with a cone which has the same height and base as the cone. The cylinder will actually only fill after 3 whole pours. So that’s why ... 〒(pi)r^2h - cylinder’s volume and 1/3 〒(pi)r^2h - cone’s volume

[@husseinsabrie3407]

the volume of the cone 1/3 of the volume of cylinder and did you get 5 pi

[@wilhufftarkin8543]

One thing that still baffles my mind is, WHY exactly is it 1/3?? If you take a 2D cross-section of a cone within a cylinder, it's basically a rectangle with a triangle within it. You can bisect the triangle into two equivalent mirrored triangles and you get two rectangles that are halved diagonally. If you add all the resulting triangles together, you should get 2/4 or 1/2, not 1/3. Yes, it's not 2D but 3D, which is a whole other story, but if you circle this whole thing around, I still don't understand how you get 1/3, even though it intuitively makes sense.

[@lolthehihi929]

I am also wondering the same thing.

[@irlallan]

I'm not sure but I'm pretty sure that we can test it, like try finding a funnel, and then a big cylinder like a water bottle, gallon jug of water etc. Put it inside, then figure out the volume of the cylinder, then the volume of the funnel. It won't be as accurate, but it will give you an idea of how it works. But still, like you said, it intuitively makes sense, though visually, it doesn't. Hope this helps!

[@wilhufftarkin8543]

@@irlallan That's probably how the ancient Greeks did it.

[@aishanasreen464]

Thank you sir.your teaching is very best

[@itsbillie1968]

Helped so much thanks

[@figueroabryan8656]

tyvm bro!

[@sumaysethia7693]

Nice vid pretty helpful

[@vidmaster011]

Bro...if I didn’t come across this video in 10th grade I would have dropped out...the formula kept pissing me off. I ended up putting .3 and 1/3 in my calculator and kept giving me dumb answers. I finally put in a 3 and got it right. Phew...

[@gaurav.raj.mishra]

👍

[@antonioquadrado734]

but WHY is the volume of the cone 1/3 of the volume of cylinder?

[@kat5607]

if you take 3 cone of same volume melt it and then mold it into a cylinder it will be equal.

[@anteconfig5391]

I know right. I need some mathematical proof. So I made some up. I presume that the VOLUME of a cone is the AREA of a triangle times the length of the circumference of the circle created by the cone. sooooo AREA of a triangle (I'll call the base "r") = rh/2 circumference of circle = 2*pi*r when you multiple these together you get 2*pi*r*r*h/2 or h*pi*r^2 for some reason when I crunch the numbers I get TOO MUCH SPACE (???) hmm idk what to do.. So I pretend that the reason I get to much space is because I accounted for "r" twice in the equation OR because the amount of space I have is the volume of a 4 dimensional cone (I'm not sure if that true but....... ...) so I divide by 3 (because Length * Width * Height = the volume of a 3 dimensional object) and get the proper answer. h*pi*r^2 / 3 or 1/3 * h*pi*r^2 In other words... I'm in the same boat as you. I need mathematical proof.

[@tamircohen1512]

I'm a year late but there are videos which explain this using calculus. If you're still interested and still don't know check them out.

[@andresrebata1958]

its not a rigorous proof but u can think of how in 2d a triangle is half the area of a square with same height and width bc as the hypotenuse reaches the "peak" it loses half the area since its in 2 dimensions. Kind of the same happens with a cone but this time in 3d so as the side reaches the "peak" it loses 1/3 of the area. Hope this helps

[@jasonvirasami1444]

Neko Master but it looks like 1/2 to me

[@queeniefredabjumalon4615]

Thank you so much khan academy because I learn advance for your KZbin and very understanding thanks for all 😊♥️

[@friendsotsegolakeroute8032]

Another formula is: B x 1/3 x h.

[@johnpark1520]

friendsotsegolake/ route 80 It's the same formula. Base = pi × r squared.

[@maadhavsharma4055]

good video

[@bharatpatel6594]

Your welcome

[@naveenrajg1002]

haven't told about that 1/3? generally people have doubt in this factor.

[@thomasdeng7659]

how did you get that cool calculator?

[@chideranwosu211]

It is a Texas Instrumental. You can get it off Amazon

[@m4x970]

His handwriting on a pc is better than mine irl

[@NoahGoldsmith]

The height and radius were the same??

[@kat5607]

nope its almost same

[@sangitathapa588]

Yes

[@kat5607]

correct me if i am wrong. volume of cone could also be area of a cross section of the triangle i.e. !/2*base*height multiplied by 2 pi ?

[@astrq1un3]

Cole Phillips honestly, your an idiotic nosy bully. go away. She/he just wants to actually succeed in life, unlike you.

[@gainknowledge2999]

How can you take capacity instead of volume?

[@dhanvant.p.s6242]

Why can't we calculate the volume by , circumference of the base × area of the right angle triangle = 2πr × rh/2

[@galacticcuber2058]

becayse it doesnt staay constant throughout the calculation. In a cylinder, you can multiply the base times the height because the base stays the width throughout the whole shape. In this case, it gets smaller, so you cant have a constant multiplication through the triangle.

[@mdzisantanvir9239]

@@galacticcuber2058 no he isn't talking about multiplying the circles area with the height, (we do understand that the circular area is decreasing)

[@mdzisantanvir9239]

Exactly my question, the triangle is moving by the circumference therefore it's only logical that it's (triangle's area x circle's circumference) which would be piR^2h instead they just assume that it's 1/3 part of the cylinder 😬

[@friendsotsegolakeroute8032]

Because 3 cones fit in one cylinder .

[@stellar8689]

prove it.

[@vol230]

@Charlez Rosa mathematical proof?

[@SFK_CHEESE]

Who is this man I goota know

[@mohammedsalih6771]

It's not clear that the cone is 1/3 of cylinder. No way to be sure. 🤔

[@rikasoft]

Goat

[@onlydreams4328]

How did you get 131?

[@daniellarson9526]

Guys

[@redstallion415]

How/why is dividing by 1/3 the same as multiplying by 3?

[@biged680]

because dividing by a fraction does the opposite just like multiplying by a fraction would divide it

[@sazidhasansafwan]

reciprocal bro

[@hollymiller2557]

Heart this comment PLZZZ DUDE we use this at school all of the time

[@kamilavazquez7772]

hi

[@brendano.2040]

+Kamila Vazquez Hello

[@Gnerf]

A cone is half the volume of a cylinder

[@heshamacademy7396]

dear salman khan i have a FORMULA to FIND AREA of cone of 2d shape. i m hesham

[@aaryama3758]

HESHAM ACADEMY ddssssss

[@neetu.mishra.]

Not visible

[@havehope646]

Jesus loves you ❤️

[@CrisisMonday]

Whenever I try to write on the computer, I get chicken scratch.

[@esmeliars]

Hes using a drawing tablet

[@bread9418]

69 comments Nice

[@gaypp6175]

65

[@gaypp6175]

66

[@gaypp6175]

67

[@gaypp6175]

68

[@soho1080]

You’re just reciting the formula.. not explaining why it is such. No good.

[@tye2953]

Slow down ffs,

[@Chinmoy-Saha]

Kire bangir put, eta integration diya korli na kn?

[@Aadhyavyasasa]

nice video