yego.me
yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Volume of rectangular pyramids using cubes | Grade 7 (TX TEKS) | Khan Academy

less than 1m read
·Nov 10, 2024

We'll be exploring the volumes of rectangular pyramids today with cubes and rectangular prisms. This is a cube; all the sides are the same length. To find the volume of a cube, I can multiply the length by the width by the height. For example, if the length of the cube is five and all sides are the same, then to find the volume I would do 5 * 5 * 5 = 125 cm cubed.

I can break this prism into three rectangular pyramids that are all congruent. So now we have a cube that's actually made out of three rectangular pyramids, and we can see here that all of the rectangular pyramids are congruent. The base of each rectangular pyramid is a square. The square is the same size as one face of our cube, and they all have the same height.

Since all of these rectangular pyramids are congruent, they all have the same volume. To summarize so far, three congruent pyramids can form a cube, and the volume of one of the pyramids will be 1/3 the volume of the entire cube. This is true for all cubes, but what about other rectangular prisms where the sides have different lengths?

15 Ways to Master the Art of Decision Making
The Psychology Of The Anti-Hero

More Articles

View All
Zach Sims at Startup School NY 2014
[Alexis] I have a distinct privilege right now to introduce another one of those New York Y Combinator Company’s CEO. This is Co-Founder and CEO Zach Sims, who started Codecademy. You guys hopefully all know about Codecademy. If programming is the fluency…
The End Of Credit Cards | A Warning To Credit Users
What’s up, guys? It’s Graham here. So, as many of you know, I take my credit card usage very seriously. And I say the term “usage” because when I tell people I have a hobby collecting credit cards, they look at me as though I’ve gone crazy and have a pro…
Keep It Simple
Imagine you woke up to two incredibly loud beeping sounds: your smoke detectors going off. You can smell the fumes rising up and filling your entire house. Your home is about to be engulfed in flames. When your body’s adrenaline kicks in, do you remember …
The Hessian matrix | Multivariable calculus | Khan Academy
Hey guys, so before talking about the vector form for the quadratic approximation of multivariable functions, I’ve got to introduce this thing called the Hessen Matrix. The Hessen Matrix, and essentially what this is, it’s just a way to package all the in…
The Cleverest Productivity Hack | Productivity Hacks for Students
This is a good idea. So, I used to buy this gum from the grocery store, and it was just like regular Wrigley’s Extra or whatever. But it was my study gum, so I only studied it when I chewed it, and I only chewed it when I was about to study. It was like m…
What's WRONG With This Cat ?!?! IMG! #21
Every geek’s dream and a great reason to keep driving your car! It’s episode 21 of IMG. Here’s a picture of Darth Prime, and here’s Barbie as a homicidal sociopath. Not terrible enough for you? Then check out this example of bad parenting. What’s this ki…