4πr^2 video explanation kzread.info/dash/bejne/aHmus6edcrvFY5M.html At first the sphere isn't rounded because it is made of a few pyramids. The trick is to increase the number of pyramids while maintaining the same radius therefore the bases of the pyramids become smaller. By increasing the number of pyramids and the bases are getting smaller, so the collective shape of the pyramids gets rounder and it resembles more the shape of a sphere. If we have an infinite amount of pyramids then the volume of the pyramids eventually becomes equal to the volume of a perfect sphere.

@aguyontheinternet8436

2 жыл бұрын

Thanks for the surface explanation

@bushraayman2587

10 ай бұрын

Asslam o alikum. Thank you for the video. Have a good day.

You seriously in a nutshell said: "a quick explanation why the surface area of a sphere is 4pir^2 is because of the amazing fact that surface area of a sphere is actually 4pir^2"

@mariopires8560

5 жыл бұрын

that explanation requires another video, right?

@AaronHollander314

5 жыл бұрын

kzread.info/dash/bejne/eYKXqMx_ndSrk5s.html

@nyomanaryasejati2550

4 жыл бұрын

Lol v: Here the explanation about surface area of sphere kzread.info/dash/bejne/aHmus6edcrvFY5M.html

@CASH-TO-THE-MERE101

4 жыл бұрын

VidyVid 👀

@swalbi1579

4 жыл бұрын

Exactly my thought. You don't explain one thing by throwing another question into the room.

I love how you concisely and accurately explained the concept of an integral without ever mentioning calculus.

@obilisk1

4 жыл бұрын

It's a really nice application of Archimedes' method for finding the area of a circle

@emmawatson9180

3 жыл бұрын

A R T

@AlexandrBorschchev

3 жыл бұрын

Ok nerd

1:20 This is the most beautiful thing I've even seen in a math channel.

@howtungchong174

7 жыл бұрын

agreed

@goncalofreitas2094

6 жыл бұрын

Me too

@ksrinivas1729

6 жыл бұрын

me too

@sujitujitbista2379

5 жыл бұрын

SUMYIU li

@AaronHollander314

5 жыл бұрын

Check out 3Blue1Brown

Day XX of quarantine, learning how to find the volume of a sphere

@user-oi7sf1jm3h

4 жыл бұрын

You will be einstein by the end of it

@blackcat5771

4 жыл бұрын

@@user-oi7sf1jm3h lol

@jamesdesantis9420

4 жыл бұрын

We all gotta keep busy!

@rickdearmont9950

4 жыл бұрын

Exercise the mind!

@puretwr899

4 жыл бұрын

Me too !

0:26 this version of interstellar brought to you by mathematicsonline

I love your animation. Surely, students will understand how the formula is obtained. I wish you would make similar videos for other formulas.

Great visual proof sir! I like the ways you derive the formulas by simple methods that anyone can understand. Good job

If we have an infinite amount of pyramids then the volume of the pyramids eventually becomes equal to the volume of a perfect sphere. And I do have a video response explaining the surface area of a sphere, thanks for watching.

@anilkumarsharma1205

4 жыл бұрын

where are tangent theta ,please tell me about it🔬🔬🔬🔬🔬🔬🔬🔬🙏

@lelouchlemprouge6380

4 жыл бұрын

why cant we integrate

@CalculusPhysics

4 жыл бұрын

Anime Movies and series This is explaining what the integration is doing. most people have no idea what integration is, and even if you do, just showing an integral isn't helpful or intuitive

@emmanuelkuzniak4534

4 жыл бұрын

Great video. But even if we have a lot of "pyramids", they are never real pyramids because there is always a very small round part at the base. Where is the sum of these tiny round parts in the formula ?

@camillefailes54

2 жыл бұрын

@@emmanuelkuzniak4534 I think that's why calculus eventually gets involved, to add up all those little pieces (pretty much integration, but not precisely)

Volume and Surface of sphere with Integrals: Koords of a sphere: x=R*sin(a)*cos(b) a=[0,2*Pi] b=[-Pi/2,Pi/2] y=R*cos(a)*cos(b) z=R*sin(b) derivatives of a: x=R*cos(a)*cos(b) y=-R*sin(a)*cos(b) z=0 derivatives of b: x=-R*sin(a)*sin(b) y=-R*cos(a)*sin(b) z=R*cos(b) crossprodukt from derivatives of a and derivatives of b: x=-R²*sin(a)*cos²(b) y=-R²*cos(a)*cos²(b) z=-R²*cos²(a)*cos(b)*sin(b)-R²*sin²(a)*cos(b)*sin(b) =-R²*cos(b)*sin(b)*(sin²(a)+cos²(a)) =-R²*cos(b)*sin(b) norm n of this vector: n²=x²+y²+z² =R^4*sin²(a)*cos4(b)+R^4*cos²(a)*cos4(b)+R^4*cos²(b)*sin²(b) =R^4*cos²(b)*(sin²(a)*cos²(b)+cos²(a)*cos²(b)+sin²(b)) =R^4*cos²(b)*((sin²(a)+cos²(a))*cos²(b)+sin²(b)) =R^4*cos²(b)*(cos²(b)+sin²(b)) =R^4*cos²(b) n=R²*cos(b) calculation of surface area A and volume V of the sphere with integral: A=int(int(n,a=0..2*Pi),b=-Pi/2..Pi/2) =int(R²*cos(b)*2*Pi,b=-Pi/2..Pi/2) =R²*sin(Pi/2)*2*Pi-R²*sin(-Pi/2)*2*Pi =2*Pi*R²*(sin(Pi/2)-sin(-Pi/2)) =2*Pi*R²*(1-(-1)) A=4*Pi*R² V=int(A,R=0..r) =4/3*Pi*r^3-4/3*Pi*0^3 V=4/3*Pi*r^3 Yea, i'am bored and have no gf

@SoYuan

7 жыл бұрын

wtf.... wow

@MrHenryG123

7 жыл бұрын

you could also just say volume is the integral of the surface area since he jut blatantly uses the surface area formula here

@christinadc

7 жыл бұрын

Philipp Petsch Have u copied or written it yourself??? OMG !!! I was just shocked. I think you could be the boss of mathematics hmmm... 👍👍👍👍😊😊😊😊😊😊 But I haven't understood even a bit(Lol)😕😕😕😕😕😕😕😕

@melonenlord2723

7 жыл бұрын

Christina DC thank you for the compliment. :) Didn't copy it, but when you know how integrals work, then it's not that hard. Had to learn this staff last year and so i know it. But please don't be sad, at first, for me it was hard to unterstand too. It takes some time and explanation. I only gave formula here. I can try my best to explain some more of what i did here if you want, but I can't guarantee that it helps, because for me it's not easy to explain something in english. It's not my main language and google translate sucks sometimes. :D

@coolguy4989

7 жыл бұрын

Philipp Petsch did you seriously just calculated how to calculate the area of a sphere with trigonometry in a KZread comment section? Man you must be really bored

Excellent! Visuals, explanation, pacing, structure of the presentation - I can think about spheres differently now thank you so much 🎉👍🍻

It's very helpful and nice. May I ask you, which Programm do you use to do the graphics?

Came across this video while researching for an assignment, and wow, your channel's very interesting!It seems like you explain the steps behind the formulas,and I really need that to solve math problems.

I was really ashamed inside that I didn't know why the formula of sphere's volume is that. I thought they taught but I forgot how they derived it but it turns out, they did not. They just made us memories the formula. This is so dope thank you.

Lol "and the amazing fact is, the surface area of a sphere is equal to four of these circles!"

@user-tt6mq1go3s

2 жыл бұрын

Yeah but how ?

Clear, easy to understand, excellent presentation...very cool :-) Thank you!!!

Nice demonstration, good work, well done :)

Really appreciate your visualizing work, it makes me understand a lot better!

Very nicely presented! Visuals are quite awesome, illustrative, and creative. Spheres are quite fascinating, even eerie, which is why they are sometimes called SphEeries. Similarly, circles are often called Quirkles, because they are quirky! Of course, Calculus provides more rigor in solving this vital volume problem, but the visuals here have plenty of helpful VIGOR to help people get to more RIGOR! Thanks for all your dedication to edication (oops, education)!

Your visualisation is beautiful, keep it up!

Thanks for the video. Love the graphics. Well done

amazing work man but you didnt explain why the surface area of the sphere is 4 of the circle area. but thank you any way for your efforts.

@TonyStark799

8 жыл бұрын

+ricky bobby That's not the topic of the video.

@Pankaw

7 жыл бұрын

There's another video where he explains that

@realityversusfiction9960

7 жыл бұрын

Elementary Foundation Stone Of Differential Geometry Given a 120 centimeter Diameter multiplied by three, the length of the circle will be 360 centimeters. Given 360 degrees to the circles length, each degree will be one centimeter in length. And not one or any number of mathematicians, geometer's or geniuses can alter or change the fact that; A circles length is exactly three times that of its diameter length. Area of a 120 centimeter diameter Circle 3 X r2 (Three times the radius squared) 120 cm x 120 cm; Square = 14. 400 sq cm 1 right angle = 120 cm x 120 cm ÷ 2 = 60 cm radius 60 cm x 60 cm = 3,600 sq cm 3,600 sq cm x 3 = 10, 800 sq cm to the area of the Circle Which is three quarters of the area to the 14, 400 sq cm square. In sum A Circles Area is always three quarters of the area gained by squaring its diameter length. A circles length is always three quarters of the perimeter length gained by squaring its diameter length. Twelve Steps From The Cube, To The Sphere (Volume & Surface Area) Calculating the surface area and volume of a 6 centimeter diameter sphere, obtained from a 6 centimeter cube. 1. Measure the (a) cubes height to obtain its Diameter Line, which in this case is 6 centimeter’. 2. Multiply 6 cm x 6 cm to obtain the square area of one face of the cube; and also add them together to obtain the length of perimeter to the square face = Length 24 cm, Square area 36 sq cm. 3. Multiply the square area, by the length of diameter line to obtain the cubic capacity = 216 cubic cm. 4. Divide the cubic capacity by 4, to obtain one quarter of the cubic capacity of the cube = 54 cubic cm. 5. Multiply the one quarter cubic capacity by 3. to obtain the cubic capacity of the Cylinder = 162 cubic cm. 6. Multiply the area of one face of the cube by 6, to obtain the cubes surface area = 216 square cm. 7. Divide the cubes surface area by 4, to obtain one quarter of the cubes surface area = 54 square cm. 8. Multiply the one quarter surface area of the cube by 3, to obtain the three quarter surface area of the Cylinder = 162 square cm. CYLINDER TO SPHERE 9. Divide the Cylinders cubic capacity by 4, to obtain one quarter of the cubic capacity of the Cylinder = 40 & a half cubic cm. 10. Multiply the one quarter cubic capacity by 3, to obtain the three quarter cubic capacity of the Sphere = 121 & a half cubic cm, to the volume of the Sphere. 11. Divide the Cylinders surface are by 4, to obtain one quarter of the surface area of the Cylinder = 40 & a half square cm. 12. Multiply the one quarter surface area by 3 to obtain the three quarter surface area of the Sphere = 121 & a half square cm, to the surface area of the Sphere Confirmation by Weight Given that the 6 Centimeter Diameter Line Sphere was obtained from a Wooden Cube weighing 160 grams, prior to it being turned on a wood lathe into the shape of a sphere The Cylinder of the Cube would weigh 120 grams The waste wood shavings would weigh 40 grams Given that the Cylinder weighed 120 grams The waste wood shavings would weigh 30 grams. Note: And ironically you can also obtain this same result by volume, using Archimedes Principle. www.fromthecircletothesphere.net

@k0pstl939

6 жыл бұрын

he did that in annotated video

@JayOnCamera

5 жыл бұрын

Yes he did... Watch it again man, and all the way through.

Your videos are awesome and very informative on a different level from most explanations, Thank You.

Love this channel. I learn each day something new.

I'm mesmerized. I was looking for this kind of explanation from my childhood. Thank you so much.

This is what real mathematics is. We were so unliky that our teachers never demonstrated these concepts while were were learning at college. I love maths from my childhood, but our teachers were unable to show us the beauty of mathematics, and I lost the chance to build a career based on engineering subjects, and ended up becoming management graduate. However, there is a saying that you are never too late to learn something...so now I am learning these amazing techniques and teaching students these beautiful techniques of mathematics...

I don't know a lot of english myself and i understood your lesson 1000000000000x times better than any other video in my language, 1000^999999 times thanks!

I think that this is just a (nice) algebraic trick because you can't divide a sphere into equal sized square-based pyramids.

Im 14 and my maths teacher wanted usto make a presentation about this and this video really helped me understand the steps. thanks man x

@TahirKhan-jq7qv

8 жыл бұрын

Same but I'm 10

@tristanhidalgo8463

7 жыл бұрын

Same but I'm 3

@Saltofreak123

7 жыл бұрын

I'm a fetus

@fatihsezer4155

5 жыл бұрын

I am a sperm

@ForfunckleStudios

5 жыл бұрын

I am the parents of myself

I loved the explanation for the surface area formula. First time I see a proof by amazement.

Superb work guyzz, finally found the type of explanation that i dreamt of but never had experienced , thank you soo much for making it mathematicsonline

The best explanation can be shown with integrals

@chrislor2882

4 жыл бұрын

This one its better, its more intuitive

@Leonardosanchezandre

4 жыл бұрын

we are stupid

Brilliant visuals! Thank you! I am sharing this with my students. :)

A very brief & to the point explanation. Keep it up!!!

Wow, this is as great explanation. Thanks! I like knowing where the formula comes instead of just blindly accepting it.

Beautiful explanation. Well done!

Thank you so much mathematics online! Beautifully explained.

Brilliant !.... Why haven't I got a teacher like you, when I was at school ?..... You are fantastic.... Thank you so much for that magic video... :-) From Brussels, with Love....

This is why I failed geometry in high school. I watched the video twice and it still makes no sense to me. I never had a problem with algebra, but geometry just makes my mind shut down.

Outstanding explanation and your graphics are very helpful. Well done!

2年ぶりに見つけた、、！ This video is easy to understand!! Thanks☺️

Wonderfully explained and very nice presentation.

Great mathematician. Thank you so much for this .

So simple and beautiful. thank you.

I totally agree with your method, which is exactly what I was saying, the calculus (integration) method is the most complete and thorough. The limit of the length of one side of the base is 0, eliminating the curved surface effect. We agree ! :-)

This video has been really helpful! thank you

Waiting for explanations like these for a long long time....................Thanks Best videos ever!! Wish this concept could be applied to other areas of study!! Pure Genius Thanks so much.

Great animations!

I love your videos Thanks for fabulous work We could ascertain which we can not imagine alone.

Amazing explanation! Pls keep it up and do more these explanation vids

Thank you so much! You explained everything in detail

This is Such a Great Help!!

Spectacular demonstration. Math is beautiful if you understand it. Using the pyramid amazed me ❤

Thanks so much for the video....this is the first explanation about this that I have understood.

This is quite an amazing explanation👍

this was soooooooo goood!!! so easy to follow and understand like this TY

extremely well explained, and its even entertaining and calming

@dragsterbixing2584

4 жыл бұрын

I think you just loved the animation there is no sense in the proof though

thanks! keep up the good work!

Awesomely explained

very very good and easy to understand. Thank you.

Bravo! Beautiful high school level explanation of how to derive the spherical volume formula from the surface area formula.

@mathematicsonline

2 жыл бұрын

Glad you liked it

Thanks man. Liked your explanation.

Thanks for the grest video...you've made it much clearer for me

Enjoyed the explanation and graphics

These in depth proofs are awesome.

How wonderful idea!! If we can think of this idea, we don't need to do any (inaccurate) experiment. Thank you for sharing.

I understood it . Nice video. Thanks for explaning . I actually wanted to know that how the formula derived .

great simple and clear

This is amazing animation!

for a class 9th student, ur videos for surafce areas and volumes are perfect.....amazing videos

Just wanted to say: this was an EXCELLENT explanation, and superbly animated. You've done a really great thing here--thank you for making this!

Excellent! It helped me a lot. Thank you.

Amazing visualization sir.

Marvelous, Never seen like that...... good work Thanks for spread this knowledge world wide through world wide web. Excellent from my side.

Thank You for making math formulas vivid and clear

Thank you *so* much for this video, it helped me a lot and relieved a lot of stress from me 😊

Very good. Nice

Thank you fo explaining. You just earned another subscriber

Well presented!😊

Really good video. Thanks!

nice it will help me with my math quiz! THANK YOU

AWESOME WORK!

Excellently explained thank you....

I love proofs.

@dineshmutha4475

10 жыл бұрын

surface area of sphere cut at h height from crown

@liliacfury

6 жыл бұрын

Same!

@ambadasdoddi6968

4 жыл бұрын

Very nice

@CASH-TO-THE-MERE101

4 жыл бұрын

Nicole Melendez Pena 👍

@ripinpepperonies9754

4 жыл бұрын

V lmao

wow wow wow.....n times wow......my heartiest wow to your process of explaining as well as the animation 👍👍👍👍

You gived s sensation of how it feels entering a sphere

This channel is just absolutely beautiful.

Excellent explaination.

A VERY GOOD EXPLANATION FOR THE DERIVATION OF THE FORMULA OF VOLUME OF A SPHERE.IT IS THE BEST METHOD A BEGINNER CAN UNDERSTAND THE DERIVATION OF VOLUME OF A SPHERE FORMULA. EXTREMELY USEFUL FOR STUDENTS.

Thanks for this great work. With which programm did you make this animation?

Great explanation........the learner would really appreciate the video...more videos please...thanks and God Bless

very nice video !! plzz make one on cone also

Thanks for this very lucid example

Just learned more in a few minutes than I did in all of high school math. If only teachers could have explained it like this and not to like 30 other kids at the same time

Even this video Looks so Good in Corona Lockdown

Thanks for this watered down derivation.

thank u a ton ur video truly helps me with understanding maths and solveing problems & i really enjoy watching it becauce they are so interesting to watch and made me imagine all the details , I'm so thankful hope u all the best

This video is really amazing.

Hey, What software did you use? Looks Awesome.

excellent video! thanks