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?

Analyzing problems involving definite integrals | AP Calculus AB | Khan Academy

Proof: perpendicular lines have negative reciprocal slope | High School Math | Khan Academy

View All

Safari Live - Day 238 | National Geographic

This program features live coverage of an African safari and may include animal kills and caucuses. Viewer discretion is advised. This is why the inclement ride is such a firm favorite. It’s Quito. [Music] It just looks ready for a fight. [Music] This is…

One of the Most Important Decisions You'll Make (Hint: It's About Love)

Who do we give our love to and who do we receive love from? I think it’s a huge decision, the most, maybe the most important one, one of the most important decisions. I use the word love. Um, I think different people mean different things by love, so I’m …

YC Women in Tech: Breaking Into Product

All right, hi everyone! It’s, uh, thanks for joining us today. I’m Captain Yala. I’m excited to have you join us for our work at a startup panel on getting into product. We have three PMs with us today and will be joined also by YC alumni Helena Merk, and…

Celebrating Earth Month—and Jane Goodall’s 90th Birthday | ourHOME | National Geographic

Hey, everybody. Bertie Gregory here… Hey, everybody! From the Greek Theatre in Los Angeles. We’re here to celebrate Jane Goodall’s 90th birthday. Hey, Jane. How are you doing? I’m here with my friend Andy. Hello! And we’ve got a couple more friends out he…

15 Traits of a Bad Life (2023)

If yesterday we talked about the good life, it just makes sense to look at the other side of the coin. The worst thing one can do is reach the end of their existence and realize they never lived; they were just alive. Along the way, by the end of this vid…

Worked example: differentiating polar functions | AP Calculus BC | Khan Academy

Let r be the function given by r if theta is equal to three theta sine theta for theta is between zero and two pi, including zero and two pi. The graph of r in polar coordinates consists of two loops, as shown in the figure above. So let’s think about wh…

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

More Articles