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?

Are We In An AI Hype Cycle?

The Dark Side of Everyday Things | Why We Can't Have Nice Things Anymore

View All

Beautiful “Underwater Kaleidoscope” | National Geographic

I was inspired to be an ocean explorer from a very young age. We had a swimming pool in my backyard, and I would put on a little mask and fins and pretend I was Jacques Cousteau or I was swimming with sharks or dolphins or something. I had somewhat of an …

The Stock Market Is Broken

What’s up, you guys? It’s Graham here. So, we got to take a moment and talk about something serious—something that no investor wants to think about, something that’s happened in the past but many people feel is going to happen again in the future. And no,…

15 Lessons From Businesses That Fell From Grace

Once they were giants. Now, their jokes from FTL trading to Kylie Cosmetics, Theranos, and beyond. We can learn a thing or two from businesses that scaled quickly and came crashing down faster than you can say billionaire. Some of these companies are stil…

Epic Grand Canyon Hike: A 750-Mile Challenge (Part 1) | National Geographic

I’m going to be honest. I’m not sure I really like hiking that much. With a heavy pack, no trail, and no guarantee of water, it’s hard, stressful, and very slow. Sure, hiking can lead to some zen-like moments, but not so much if you’re lost, really tired,…

Andy Grammer JUMP Earth Day Performance | ourHOME | National Geographic

What if I jump? What if it works? What if I’m meant, meant to be more than patient, more than patient? I’m biting my tongue, holding my breath. I think it’s time we had a conversation, a real conversation. Here it go! Make a choice, make it loud. Home is…

Text Messaging Helps Elephants and People Coexist | National Geographic

You know India has the highest number of Asian elephants, and there are millions of people living very close to or within the elephant landscapes. Between 1994 and 2015, 41 people lost their lives in direct encounters with elephants because people didn’t …

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

More Articles