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?

MARS: Humanity's Most Dangerous Mission

Molecular solids | Intermolecular forces and properties | AP Chemistry | Khan Academy

View All

The Cosmic Connectome | Cosmos: Possible Worlds

[Horn honking] [Siren wailing] A city is like a brain. It develops from a small center and slowly grows and changes, leaving many old parts still functioning. New York can’t afford to suspend its water supply or its transportation system while they’re bei…

How we maintain discretion at The Jet Business.

I’ve met with a lot of famous people and celebrities both personally in my social circles and professionally. But, of course, most people who are buying or selling their airplane are pretty confidential about the situation, so we usually don’t try to shar…

French and Dutch colonization | Period 2: 1607-1754 | AP US History | Khan Academy

Although the Spanish were the first European colonists in the New World, they didn’t remain alone in the Americas for very long. Just three years after Hernan Cortez captured Tenochtitlan, the French government sent its first explorer to poke around North…

Gmail Creator Paul Buchheit On AGI, Open Source Models, Freedom

It seems like Google has all the ingredients to just be the dominant AI company in the world. Why isn’t it? Do you think OpenAI in 2016 was comparable to Google in 1999 when you joined it? Are you a believer that we are definitely going to get to AGI? Wha…

Worked example: problem involving definite integral (algebraic) | AP Calculus AB | Khan Academy

We are told the population of a town grows at a rate of ( e^{1.2t} - 2t ) people per year, where ( t ) is the number of years. At ( t = 2 ) years, the town has fifteen hundred people. So first, they ask us approximately by how many people does the popula…

The Middle colonies | Period 2: 1607-1754 | AP US History | Khan Academy

Over the course of the 1600s, the English continued to settle along the eastern seaboard of North America. Now, we’ve already talked about the settlements at Virginia and those of Massachusetts, and a little bit about the settlement of New York, which was…

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

More Articles