Visualizing the Volume of a Sphere Formula | Deriving the Algebraic Formula With Animations 

I never knew that two identical cones are equal to the sphere of equal height and equal radius. That is very useful to know. As a 3D modeller, I can imagine squashing a cone to make hemisphere.

Excellent work for all Nations

This was so simple and well explained. The visuals did great too. Thank you.

I wish all mathematical formulas could be explained in such an intuitive way- Many many thank you's

Anyone here from India?

Thanks for making me understand the proof of the formula for the volume of a sphere. This was interesting.

After searching so many video finally got the right place Thank you so much God bless you

First time I understand their volume properly thanks and God bless you

This is best method to explain maths and geometry, and am sure this method will break tanoo in learners that maths/ geometry is very difficult subject. It's teacher's duty to discover right method to explain the subject, and think this is the most effective way. Thank you very much for the video and wish you best of luck in your endeavours. Namaskar.

Dear Sir God bless you for sharing your knowledge. I'm a retired engineer trying to fill any gaps in my head. Lol. I think that you're the answer. Smile. I'm going to subscribe and view all of your work. Much respect. Great channel.

This is great. Presented beautifully slowly and carefully so you can actually follow it. Love it.

WOW!! This was so coooool to learn. Thanks for such a clear explanation and clear visuals! My 6th grader was asking me where does the 4/3 come from, and now we both know! :)

I think my eyes just got blessed

8 years later, still the best video out there explaining this

Kyle... Your animations are excellent. A useful, and orthodox method of deriving the formula for volume directly.... Draw your sphere, centre (0,0). Allow sphere radius to be r. Select a value of x to the right of (0,0). Erect a perpendicular (perp) of height y. Rotate that perp about the x axis to form a disc. Allow that disc to have width dx. The incremental volume of that disc is its area A = pi*y^2 multiplied by its width dx.... dV = pi*y^2*dx The perp height y is related to x by the classical equation of a circle... y^2 + x^2 = r^2 make y the subject... y^2 = r^2 - x^2 It will follow that... dV = pi*(r^2 - x^2).dx To determine the full volume of the sphere, integrate that last equation -r to +r... V = integral of pi*(r^2 - x^2).dx between -r and +r V = pi*( r^2*x - x^3/3 ) Insert the limits.... -r and +r V = pi*( r^3 - r^3/3 - (-r^3 + r^3/3) ) = pi*( 2*r^3 -(2/3)*r^3 ) V = pi*r^3*(2 - 2/3) = pi*r^3*(6/3 - 2/3) = (4/3)*pi*r^3 V = (4/3)*pi*r^3 If, later, you want to get the surface area, simply differentiate the volume function, having identified that... dV = A*dr, so A = dV/dr dV/dr = A = 4*pi*r^2 Best... Troya.

Hello I’m in fifth grade and this was a very good way of understanding a complicated formula

Oh WOW, this is mind blowing in my opinion. As simply as you put it, it's still amazing. I'll definitely use your method in my lesson planning in the future. Thank you.

Amazing! Two cones volume is equal to a spheres.❤

Fantastic explanation. Thanks a lot.

I am 63. I really appreciate this. Thank you.

Loved this video. It was clear and easy to follow. After all these years of teaching, I have not seen such a clear explanation. Thank you!

This is soo useful man, I have to give a explanation about this tmrw and they didn't teach us about this.

This channel deserves more subscribers ...Great video.I will pray for you!

I always wondered why the volume of the sphere is calculated by that formula, and when I started to see the video where you put water from the cone into the sphere, I immediately understood what you were gonna show me. My head exploded instantly. Now I understand, thanks so much!

The proof using integration is just as beautiful as this

Beautiful, concise, clear presentation. EXCELLENT!

Amazing how simple and yet effective this was

l usually don't comment on videos but this is the BEST video I could find that explains where the formula for the volume of a sphere comes from! This helped ALOT because I do way better when I understand where the math comes from rather than just memorize a formula. Thank you so much for this top notch explanation!

Simply amazing. I wish our world has more teachers like you. God bless you

Since I haven't studied calculus yet, I couldn't understand the proof of this formula but Sir you made it really easy for students like me. Thanks alottttt!

This is the best video in math that I've seen! you make it look so easy and simple, thank you !!

Perfect animation and explanation sir... You are simply awesome

Someone finally decided to make sense out math.

OMG! I wanted to be able to visualize math forever! I can visualize Anatomy easily, but math... was hard for me to visualize. Thank you so very much! Many many thumbs up!

Wow brilliant, I love it when I see those things, now I can fully understand it instead of just accepting it

Mind Blowing, Impressive, Astonishing, Marvelous, Fantastic, Amazing, Beautiful and very easy and clear explanation. Thanks a ton for the video. May God Bless You.

Why would anyone dislike this video! This is awesome. Great job (now I don't have to memorize)

So simple but well explained! Thanks a lot!

You have a really calming voice

Thank you so much for this!! So many videos just tell you the formula, but knowing why is the key!

Yes!! This is what every teacher needs to teach. Awesome job.

Best video explaining the volume of a sphere I've seen yet! Thanks!

your wideo is not completely explains the problem, it's just that 2r=h it's doesn't explain why two cones are fulling the sphere, what about Archimedes and Cavalieri?

This was simple and absolutely great.

This really helped with our online class, thank you so much 👍

this is how it should be taught . thank you

Great explanation. But how did we find that the volume of a sphere = the volume of two cones with the same height and radeii as the sphere?

Excellent explanation and accompanying graphics

Great explanation. Thanks for making maths clearer...

I actually watched this video to find the area a come, and it was so useful!

this makes so much sense now thank you so much

It cleared my mind and proof where came the volume formula of a sphere. Love this video. 2r equals to h of the sphere was a bit difficult to understand but later understood it. 😊

Thanks you bro that's really really help me ,don't stop

This is really useful with my maths work. Thanks so much ;)!!!!!

Excellent explanation....It changed my view towards cone n sphere.. Thanks a lot sir

First you try to derive Area of circle by cutting small sectors of say 1 mm arc length. Set the sectors in alternative direction to get a parallelogram of pi x r length and r breadth which gives pi r square. In the same way visualise small cones cut from the crust centre with radius r height also r. Cut the sphere into four pieces. By arranging each cone in alternative direction, Each piece volume will come 1/3 pi r cube. Then comes 4/3 pi r cube.

Great explanation, but most of the video at the end is covered up by the ads and my students want to see...

Useful it is... Thanks so much for an easy and assertive explanation..

The effort done in explaining the concept is massive and so is the video presentation and editing ... nice work, can you tell me which software has been used for editing purposes, looks like a charm...

Osm 👍👍👍 I don't have words to express my gratitude to my new teacher thanks 😊😊 sir

wow....that was just amazing...i really understood it more clearly and better......

It"s very attractive method.Also helpful for students.

So happy I wish they teached this instead of just formulas.

I'm not sure why this is recommended to me now... But you can get around the "experimental" part by using Cavalieri's principle to show that a cone plus a half sphere yields a cylinder.

Incredibly helpful! Thank you.

I think I've just been enlightened, great explanation!

U r such a good teacher..this was best..plz make more videos..sir

What? It's very simple!! You are amazing. Yeah, more than my channel Machifa. I should say this. Clap for him

one of the most satisfying videos

Very helpful. thanks. I did not know that 2*Vc = Vs. It will be useful one day.

Trying to find the proof..Now got it in simple method sir..Tq very much

Simple and the best explanation..

Hi I'm Bangladeshi.very nice and easy delivered....so many thanks.

why did you divide it with 3 ?

Awesome explanations

Unmatchable knowledge

best explanation. makes a lot of sense

Thanks a lot sir. This video been proved a deeper understanding to me. Now i can easily remember the formula of vol of Sphere..Yayyyy !! :)

Thank you so much

Really awesome explanation

I want to thank you for your this good explanation

Always enjoyed calculating volumes, but never new of the 2 pyramid solution for a sphere . .

Best way to explain

It was really awesomesauce👍Great Sir ..... Much helpfull for us .....👍👍👍 ..

Wah sir :) English padhne ke liye Vidya Guru ke Sonia ma'am videos kafi ache hain. Unka padhaya kafi exams me aa jata hai.

Thanks for this! I know how to derive it using integrals but the visuals helped!

Wow what a wonderful and amazing explain. Thanks you.

I think we can understand many concepts and formulas with animations.

I have a question for you. Think of a roll of tape. First of all, based upon the outer diameter of the roll of tape, and the diameter of the roll of which the tape is wrapped around, and taking the thickness of the tape itself into account, you can calculate the length of the tape. The question is: Why, if the outer diameter is 7", the roll that it is wrapped around is a 1" diameter, and the thickness of the tape is 1", does the tape length turn out to be pi in feet, meaning 3.141... feet long ???

The sum of cone volume with high equal to radius (h=r) and the volume of cylinder with the same data, high equal to radius (h=r) is the same as sphere volume with the same radius (r) !

Thankyou so much its very useful to me😀😀😀 I am very happy to learn from your video Once more thankyou so much

Wonderful explanation

3) calculate the new capacity of a flat capacitor that one of its flat plates is shifted up by an angel teta less than the 6 degrees. Compare the new capacity with respect to old capacity.

Genius presentation

Good explanation. Excellent animation

I think I've understood now thanx sir.

i just loved it..thanks a lot for the efforts

your voice is so soothing

Excellent work

Very very nice video. Keep it up sir and make more amazing video like this.