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Chapter 6

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00:29

The surface area of a cube…

02:04

Find the lateral area and …

01:50

What is the volume, in cub…

01:07

Diagonal of a Cube. Find a…

01:00

01:17

Geometry The length sof on…

01:44

The side of a cube measure…

01:21

Find the volume of each pr…

01:13

For any cube with edges of…

Suppose that each edge of …

Okay, So for this one, it says, What is the total surface area of a cube if the length of each main diagonal is nine. So we know that the total surface area, So let's go and defined some terms. So surface area, it's just the total of all the areas of the surfaces. Okay, and then we know that main diagonal is the longest diagonal distance that we could draw in a cube. So here's the thing is that some people think that the main diagonal, if this is our cube, is going to be this right here. But that's not the main diagonal of Accu because that's the Dragon Office Square. And also that's not the longest it's actually gonna be from here to here, like that intents of them. Let's go in and draw out our figure and right over here. So here is my cube. Okay on, then, if the main diagnose or which is this is nine really to find the length so that we can find the surface areas because for a cube, we know that the length times the length is the area of one surface, and then there's six surfaces, so we would just do six l squared for that one. So then, from here, we need to draw some lines in order to get that. So if we draw this line right here, then we know that this a vertical line to this platform right here is going to form a ninety degree angle. That might not really look like it, but you know that if we were to isolate it out and draw it, we know that it is. So then this right here is just one length. So let's call that. Oh, and this is also something that we can find because that is made out of another right triangle, which is this part right here. Let's go and draw out that one as well. So for this one is going to be l and L, which means by the Pythagorean theorem or special right triangles. This one is going to be route Tio assuming a crime, this group to its well and then in order to find our l, we just have to do. But that green here and one more time so jaggery. And then it says that l squared plus route to el that will quantity squared is equal to nine squared. So then we know that l squared and then this square in that square cancels out plus two l squared is equal to nine squared. And then from there we know that three l squared is equal to eighty one. So from here, I'm going to fight by three on both sides. To get that l squared is equal to twenty seven. And instead of square rooting this I'm just going to keep this acid is because l squared, we know is actually the the surface area uh, one square, because a square looks like this, it's got fell. And so if we do, I'll Square that's the area. But then we know that there's six of those in a cube and so we're going to take that twenty seven and multiply that by six. And when we do that, we're going to get one hundred and sixty two. So then we know that bee is our answer. So for this one, the key is to draw a couple of lines and make a couple of right triangles and then be able to say that you should be able to use the Pythagorean theorem

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