Why is the volume of a cone one third the volume of a cylinder?

[@the_second_channel]

the animation is really "3 blue 1 brown" esque

[@SaesarCalad]

He made his editing program public recently I believe

[@1grapefruit]

@@SaesarCaladit's been public for ages afaik, just more popular recently

[@spenzr6920]

Thats because he used manim i think

[@creationgamers]

The visuals are cool

[@stas4017]

You can actually take a pyramid with a square at the base with a height of half the side of the square. Then (try it yourself) build a cube with 6 such pyramids. If the side is a, the volume of the cube is a³. One pyramid is V = a³/6 = a²h/3. Now, intuitively, the shape of the base shouldn't change the volume, only the area would. That's an intuitive way of justifying where 3 comes from without integrals. More rigorously, you can stretch the pyramid to any height, which is a linear map that would increase the volume by a factor of h' / h, so the formula for V still stands. You can also move the top of a pyramid, which is a shear mapping so it doesnt change the volume (determinant = 1). Obviously, the mapping doesnt change a and h. Now, you can approximate a cone with any shape of the base with such pyramids which yields V = 1/3 S h

[@pihedron]

I would've loved to go into more depth with the geometric proof but animating in 3D was a bit of a nightmare. You have a good explanation.

[@abshariadam]

Soo cool!!!

[@Gouzation]

Hey bro ur videos are really good but consider investing in a better mic or atleast try to filter some noise in audacity

[@pihedron]

True, I have a budget setup. I can't really buy anything yet but I'm glad you like my videos.

[@Gouzation]

​@@pihedronI have the FiFine k669b it's a 20$ mic and with audacity it sounds just as good as a 150$ one good luck bro

[@JoshyLPHD]

I understood it, but still find it too fast for me. Good video tho, keep it up.

[@nazishahmad1337]

Please provide Source Code in description.

[@zehlenmath]

That's good 👍

[@CodexMathematica]

Are you make the video with manim?

[@pihedron]

Yes.

[@spenzr6920]

Audio needs improvement and if possible, try to show visually how the change in equation affects the shape or whatever the topic is. I hope i could explain the second part properly. Good video otherwise