Volume of a Sphere, How to get the formula animation

(4/3)∏r(cubed) gives you the volume of a sphere, but where does the formula come from? Here is a simple explanation using geometry and algebra.

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[mishraonline]

Now prove How to get the formula for surface area of the sphere which you have assumed in your proof.

[Tozabon]

@antjam666 He forgot to mention that the sphere is sliced to infinite piramids, that makes em so small that the extra volume that comes from the "rounding" of the bases is reduced to zero (u may notice that the actual number of the piramids is not used at all to create the formula). How and why this works mathematically is a whole different story (It's mathematical analysis and it is about how infinity works!)...

[blueswallowtaillover]

I had to figure this out for math class, and now that I found this vid, I shall get an A while my classmates fail epicly.

[Redflowers9]

You couldn't do this by finding the volume of the revolution of a semi circle could you? 

[NITHARSUN55555]

pls send ur contact detail i want to know mre.your way of teaching really super.my mail id is nitharsun55555@yahoo.com

[Aurumk1]

@mishraonline wouldn't they tell you how many miles or so long the sphere was so you would know its base? I mean with this how do you know the area of the base.

[Dracopol]

@Scallywag1AIK Maybe you have a Macintosh or something? On any PC, Alt-227 makes pi.

[Scallywag1AIK]

@Dracopol

That makes a "Ò"

[Kosekans]

Use calulus for a more rigorous proof.

[Dracopol]

If you want to show π more correctly in your info, why not just hold down Alt and then hit (on the keypad) 227?

[yonatanalemayehu]

This is just an awesome, short and precise proof of the vol of sphere.

[shaffiz81]

how you derived that surface area is times 4?

[nejtilsvampe]

couldn't you just find the "solid of revolution" (idk if that's the word I google translated) of a half circle?

[TabIeTennis]

Wonderful amount of effort put in, I feel it really deserves much more views

[zosopick]

@Tzacharu123 Ohh, now it makes sense, thank you for explaining that to me, and possibly someone else here, on youtube :)

[Tzacharu123]

@zosopick Correct, it is curved. However it is a close approximation if you have a small enough base. This is where calculus comes in, because it deals with the infinitely small and infinitely large. You can come to this same equation using calculus, assuming there are an infinite number of pyramids, rather than a finite amount, which is what this video does ("n" pyramids).

[WSWarthog]

@zosopick

I suspect limits must be involved. As the length of each side of the base tends to zero, the curvature in the line tends to zero and the volume of the "pyramid" tends to the volume of an actual pyramid.

[zosopick]

The ball is curved, so how to they get a pyramide? The base of the pyramide is curved. so it's not a pyramide

[Mathemaphysicist]

@Tozabon Oh wait, when you said analysis, did you mean evaluation of limits? If so, then I'd be interested if you could write out the limit which you are talking about (and I don't just mean writing out the integral of the total surface area of the sphere, in terms of limits! :P)

[Mathemaphysicist]

@Tozabon Hey, most of us are applied Mathematicians not pure! Topology doesn't interest us! :P

[Mathemaphysicist]

@Tozabon Slicing a sphere infinitely many times would produce infinitely many circles, of several radii. The sum of the diameter of these give the surface area of the sphere, and the sum of their area give the volume of the sphere. However, we don't know how to define the radii of each circle, so I can't see how this model will help.

[Mathemaphysicist]

@antjam666 No, if you want to form the tightest packing structure on the base of the pyramid, such that there are no gaps (which would correspond to empty volume). If you think about it, the best structure would be a square base for this. And this is the structure which is used.

[Tozabon]

@antjam666 perhaps you can grasp this easier if see how the surface of a circle is mesured by slicing it to infinite pizza slices( idk if there is a video about that but it's more simple). Excuse me if i spelled anything wrong, english is not my native language.

[sondreu1]

mind = fucked