Volume of pyramids intuition | Solid geometry | High school geometry | Khan Academy 

Always great content! I love that you are explaining the WHY!!! I’ve always been inspired by your channel. I’ve admired your videos for many years and finally got the courage to start my own math channel.

This is the easiest explanation I've seen, doesn't deal with series and all that crap. Thanks!

Love this channel.Doing Geometry in class currently,I'm getting MOST of it,but the videos You have REALLY help a lot.Thank You so much.

How do you know that the left, right, front and back pyramids have also k in their equations? How do you know that these constants of proportionality are equal?

Even when i am taking precalc, calc, etc. you can still teach a dog some new tricks. Thank you so much for these videos. Keep it up

These are so great. I wish Sal was making videos back when I was in school.

Thank you for answering the WHY Great content! Love it! Would like to see another episode explaining abt the volume of a cone

I have a question. Why is the constant K the same between the different colored pyramids? Wouldn’t each pyramid have a different constant K?

Really happy to see another video from khan academy about math. I actually have a video on my channel about word problems using volume!

This is how many people use khan academy because of corona 👇👇👇

Love❤ from Nepal🇳🇵 Grateful for your videos 😃

It is fascinating to know how neat je draw each pyramid sketch using DIGITAL PEN

this is with assumption the constant is the same k for each cases.

Thankyou for these Math concepts! I’m really understanding!

Amazing video my mentor I am following your footsteps And I need your blessing to prosper

Very elegant presentation but I wonder whether one doesn't need an argument to ensure that k is somehow not dependent on the dimensions of the pyramid.

It's a bit funny how other commenters are so satisfied with the explanation and find it easy. From my perspective this is really clever and unobvious. It's not intuitive at all that you should make the assumption that the ratio k between the volume of the pyramid and the box that contains it will be the same for every pyramid. And even with that assumption it's not easy to foresee the usefulness, in finding a general formula, of expressing the volume of a box of arbitrary dimensions in terms of the 6 pyramids. You would need the intuition that the pyramids, despite differing dimensions, have the same volume. That's not obvious at all. At the end of the video I still don't see the grounds for making that assumption except to try it out and see that it works, coincidentally. Finding the formula itself is easy with calculus but it's helpful to develop these geometric intuitions edit: I think I understand why someone would find this assumption useful now. Fundamentally the assumption is that the volume of the pyramid is *linearly proportional* to the volume of box that contains it. So if you've done enough algebra, you'll know that expressing the volume of the box as a sum of the volumes of pyramids will yield a linear equation in which x,y,z will cancel out and you can solve for the constant of proportionality. It's more of anticipating a linear equation where x,y,z cancel than having the intuition that the inner pyramids have the same volume (it's impossible to tell that a-priori). That's a pretty good game plan.

Gorgeous.

I have no idea why I am watching this...perhaps I'll use it in the future

I was confused about how to get the volume of pyramids but your video helped me @Khan Academy

excellent explanation ❤️❤️❤️

A lovely pyramid scheme you have there.

Hey khan, I appreciate the video you uploaded. My question is did you drive the one-third because in an essence there are dimensions to the pyramid? So one-third times the three sides which in this you called xyz. Thanks

Wonderful.

Thank you

Good 😍😍😍

Ah😮❤22-10-2023

Does anybody know what programm he is using as a chalkboard?

Are you Khan?

....

Deleted your video

Your advertyis disturb and iam very angry of your app cut it shut up