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?

Worked example: Using the reaction quotient to predict a pressure change | Khan Academy

Foraging in the Rainforest | Restaurants at the End of the World | National Geographic

View All

No More Gas | The Worst Energy Crisis In 40 Years

The U.S. is facing a diesel shortage. The price of diesel has been soaring for months. In 25 days from now, there will be no more diesel, up 27 and 28 percent. It’s a very, very high bill. “What’s up guys, it’s Graham here.” So, in 1973, the United State…

How To Invest $500 Per Month

What’s up, you guys? It’s great here! So, I realized in many of my videos I talked about investing ridiculous sums of money or putting 20% down to buy real estate, which could work out to be like six figures in cash. But I wanted to take a different appro…

Elon Musk to Jordan Peterson: “Life had no Meaning”

So, I wondered what’s motivated you? Cuz you push in so many directions simultaneously. You have to be really highly motivated to do that. And so, you figured out that the question, in a sense, was the answer. Yeah, the question—or I said another way—tha…

Homeroom with Sal & Laurie Santos, PhD - Thursday, October 15

Hi everyone! Sal here. Welcome to the Homeroom live stream. We have a very exciting guest today, Lori Santos, professor at Yale University, who teaches a class called Psychology and the Good Life. So, it’s going to be a really interesting conversation. I …

Adventures in Photographing England's Urban Wildlife | Nat Geo Live

I’m always trying to look for flagship species, talismans to represent whole ecosystems. If you wanna photograph the Arctic, you photograph polar bears. If you wanna photograph Africa, you photograph lions. Well, you can have a wildlife experience in a ci…

Safari Live - Day 59 | National Geographic

Well, sorry about that guys. We unfortunately lost our internet signal, so we are back up and running now. Gremlins are gone, everything is all good. The sun is coming out and there’s wonderful things of foot’s shadow and cover. So, messing around with a…

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

More Articles