About this video
The video finds the volumes of two cubes with side lengths 7 m and 11 m. Because all edges of a cube are equal, the volume is side x side x side, so 7^3 = 343 cubic meters and 11^3 = 1,331 cubic meters.
You'll be able to
- find the volume of a cube when I know one side length.
- write the volume of a cube using an exponent of 3.
- give the volume in cubic units.
Key words
- cube
- A rectangular prism where every side (edge) has the same length.
- volume
- The amount of space inside a solid, found here by width x depth x height.
- cubic meters
- The unit for volume when lengths are in meters; one cubic meter is a 1 m by 1 m by 1 m cube.
- cubed
- Raised to the third power, like 7^3 = 7 x 7 x 7.
Transcript
- [Instructor] So we have two different cubes here, and I wanna figure out their volumes. For each of them, we know one of the side lengths. So why don't you pause this video and see if you can figure out the volume of each of these cubes. Okay, let's start with this smaller cube here.
We can see that this length, which we could consider its height, we could see that it is 7 meters. Now what we know about a cube is all of the sides have the same length. So if the height is 7 meters, then the width is also going to be 7 meters. And then the depth itself is also going to be 7 meters.
And if we want its volume, just as we would do for any rectangular prism, we would multiply the width times the depth times the height. So the volume is going to be equal to 7 meters times 7 meters times 7 meters. Now what's that going to be? 7 times 7 is 49, and 49 times 7, I think that's 343.
Let's see, 9 times 7 is 63. 4 times 7 is 28 plus 6 is 34. Yep, 343. So this is going to be equal to 343 cubic meters. And that is looking pretty good. Now, one thing you might have noticed, this is the same thing. This is the same thing as 7 to the third cubic meters, because 7 to the third power is just 7 times 7 times 7.
And so that's why it's not a coincidence when people see something to the third power, they call that seven cubed because that's the same thing as finding the volume of a cube if each side was 7. Now let's do it with this larger one, and I'll do that in a different color here.
The volume here is going to be, and we could immediately say based on the same idea, if one side's 11, all of the sides are gonna be 11. This is a cube, so it's going to be 11 cubed cubic meters. Or another way to think about it, it's going to be 11 times 11 times 11 cubic meters.
And 11 times 11 is 121. And 121 times 11, you could work this out if you would like, but I happen to know, and this is one of the neat properties of 11, that this is going to be 1,331 cubic meters. 1,331. How did I know that? Well, you could multiply it out, you could take 121 times 11.
1 times 121 is 121. And then 10 times 121, you could put the zero here, and you'd get another 121. You add this up, you get 1331. Another interesting thing that you could think about in the future, isn't it interesting that 1 plus 2 is 3, and that 2 plus 1 is also 3?
Another way to think about it, if you have 11, 121, 1331, you might see a little interesting pattern here. But anyway, that's not what I'm here for. I am here, and you could think about what happens when you multiply by 11 again, you might see something like this, 14641.
Anyway, I don't wanna distract you with this stuff. The whole point of this video is finding the volume of cubes, and you can see that here we took 7 to the third power, 343, that's how many cubic meters, and similarly, we took 11 to the third power, 1,331 cubic meters.
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