Volume of a Pyramid, simple explanation

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This is a simple intuitive explanation for volume of a square pyramid.

[sylvainpilon]

That is exactly what I was looking for: a demonstration of the formula. Fantastic ! Thank You !

[Attalla-tb]

It's a very simple derivation, yet this opens up my mind so much. Thanks for sharing!

[isaakb]

This is a great video but the music is a little loud .... out of balance with the words.

[MC_Transport]

Finally an explanation without using calculus! It's much more easier to understand

[gijsvandelagemaat]

This prove can be extended to strange shaped pyramids. When you scale any object for example factor 2 in one direction, the volume of that object also increases with factor 2 (to see this: just replace the object with little cubes, and scale the cubes). Since a brick is simply a cube scaled differently in different directions, the same explanation holds: 3 pyramids fit into 1 brick.

[meme]

you are the only YouTuber that actually helps with my school work

[kenhaley]

A little OVER-simplified. The six pyramids are all congruent (same size and shape) only if you start with a perfect cube. If you dont start with a cube, but another rectangular solid, you have to prove the statement that all six pyramids have equal volume.

[horacioguillermobrizuela]

Nice! short, clear and precise. Thank you! Nevermind the music

[MooMooMath]

Helpful video. Clever animations. You must have fixed the volume of the music problem because the music volume was low. I shared a link to your video on my " Demonstration of pyramid volume" video.

[mohamedamr]

best math video ever
it simply clear my vision

[samisiddiqi]

Great video! When I was watching the other video, I knew that there was a much better way to prove the volume of a pyramid which did not have to involve a series. What went in my head was that the pyramid can be inscribed inside a cube or rectangular prism flippes vertifally, but I couldn't think of an actual prood for it.

[nmmm]

Is this real proof? I don't think so. It works only for square pyramid with height equal to 1/2 of base square size.

[pressedup]

This proof only covers square pyramids, not tetrahedrons(triangular-base pyramids) or other pyramids. Would a similar approach work for them as well? Also, for this proof to work(the main argument here is that the six pyramids are equal), it must be that l=w=h, so would it work for pyramids inside a cuboid?

[cpg]

how about rectangular trapezium pyramid?why are their formulas the same u have just proved formula for square pyramid
thx a lot if u provide me with an answer

[yoonkim]

Thank you!!! This was the simplest / easy to understand pyramid explanation

[Salsahaj]

A good mathematical derivation! But - I also would have preferred it without this strange "music".

[ebrahimhamedi]

Thanks a lot.animation is a good tool to explain some of formulas.

[benribon]

This prof is relevant only for square pyramids with a ratio of 1:2 between the height and the base's length.

[BigDBrian]

This is not a complete proof, though. It only works for one specific shaped cone, the one that fits in a cube. No matter the size of the cube, it'll have the same angle and proportion of base to height.

[kingmunch]

can you show us how or the sum of all positif integer numbers is equal to -1/12?