How to Find the Diagonal Length of a Cube | Space Diagonal of a Cube, Geometry

How do we find the diagonal length of a cube? In today's video math lesson we derive the formula for the length of a cube's diagonal, also sometimes called the space diagonal or solid diagonal of a cube. A cube does have multiple diagonals, but they all have the same length! Try to prove that fact if you haven't already, it is pretty straightforward, you just need to use some triangles!

By introducing an additional line segment into our diagram, we are able to use the Pythagorean theorem on a newly created right triangle, and this is the key to the problem! Check out the full lesson for the detailed explanation.

The diagonal we are discussing in this video is sometimes called a space diagonal or a solid diagonal, which is a diagonal connecting vertices that share no common faces of the solid. By that I mean, if we look at the two endpoints of our diagonal, one endpoint is incident with three faces of the cube, the other is incident with 3 completely different faces of the cube, so they share no faces.Thus, the line segment joining them is a space diagonal.

This is in contrast to a face diagonal, which would be like the diagonal of the bottom square face which we use in the video. A face diagonal joins two vertices that are incident with a common face.

I hope you find this video helpful, and be sure to ask any questions
down in the comments!

+WRATH OF MATH+

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[saudalkaabi]

thanks mate you are better than my teacher in my opinion.

[klim]

thank you, saved my 2 hours of trying to figure out stuff from the book itself. Great video

[Rolekseditz]

Thx a lot bro u helped me a lot I was studying the night before exam and u are the saviour for me ❤

[monox]

Math problems: *exist*
Wrath of math: I am about to end this man whole career

[srishti.]

Lots of love from India amazing explanation

[AbinashDas]

Thanks for explaining so much clearly. You are not like others who makes mathematics complicated

[prabhmehararora]

Thnx Broo
I m sure that I won't forget this in my ENTIRE LIFE!!

[uranium_]

Thank you very much for this tutorial, it helped me so much while doing my homework

[itz_justinseagull]

i’m having an online quiz rn and istg they never taught me how to do that question.

[eeol]

Any retangular box diagonal is the square root of the sum of the squares of the sides or d²=a²+b²+c². This is just an extension of the pythagorean theorem. This is interesting because the diagonal as I understand it, represents time as the 4th dimension of space/time. The pythagorean formula is extended for further dimensions 5, 6, etc. in a similar manner.

[crispy_bagel]

can you do a similar explanation for rectangular solids and right cylinders?

[খামখেয়ালীমন-ব৬ফ]

Very easy to understand 😌👌. Thanks for your help

[stygian_xd]

Awesome Gonna help a lot for my exam 🙃🙃

[abdulsk]

Simple and clear explanation.Thank you👍

[opsharmag]

I really got rid of this problem...thanks a lot....im from india

[sonalipawar]

Thanks bro this is a most common type of question that comes in any competative exam ... you helped me to understand it easily... love from India ♥️👑😘

[obamaprism]

These kinds of videos save my test grade

[alitech]

Thnku sir... Alot.. Spprt
From India 🇮🇳
Your sound is so adorable💖

[monoman]

'so simple' is where some people give up

[jacearnold]

Is it really important to learn vectors and everything related to it ?