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# Rotating 2D shapes in 3D

CCSS.Math:

## Video transcript

what I want to do in this video is get some practice visualizing what happens if we were to try to rotate two-dimensional shapes in three dimensions what I mean by that let's say I started with a right triangle so let's say my right triangle looks like this so let's say it looks like that right over there and so this is a right angle and let's say that this this this width right over here is three units and let's say that this length is five units and I'm going to do something interesting I'm going to take this two-dimensional right triangle and I'm going to try to rotate it in three dimensions around this line around the line that I'm doing as a dotted magenta line so I'm going to rotate it around this line right over there so if I were to rotate it around this line what type of a shape am i going to get and I encourage you once again it's going to be a three-dimensional shape I encourage you to think about it maybe take out a piece of paper draw it or just try to imagine it in your head well it's to think about in three dimensions what I'm going to do is try to look at this thing in three dimensions so let me draw this same line but I'm going to draw it in an angle so we can visualize the whole thing in three dimensions so imagine if this was sitting on the ground so that's our magenta line and then I can draw my triangle so my triangle would look something like this so it would look like it would look like this so once again this is five units this is three units this is a right triangle I'm going to rotate it around the line so what's it going to look like well this this end right over here is going to rotate around and it's going to form a circle with a radius of three right so it's going to form so it intersects if that was on the ground it's going to be three again and let me draw it down so it's going to keep going down whoops I don't want to press the wrong button so it's going to look something like this that's what the base is going to look like but then this end right over here is going to stay at a point because this is right on that magenta lines this is going to stay at a point and so if you were to look at the intersect so it looks something like this so it look like this and then you'd have another thing that goes like this and so if we were take a section like this it would have a little smaller circle here based on what this distance is so what is the shape what is the shape that I am drawing well what you see what it is it's it's a cone it's a coin and if I shade it in you might see the cone a little bit better so let me shade it in so you see you see the cone so what you end up getting is a cone where it's base so I'm shading it in so that hopefully helps a little bit so you end up getting is a cone where the base has a radius of three units so let me draw this so this right over here is the radius of the base and it is three units I could also draw it like this so the cone is going to look like this and this is the tip of the cone and it's going to look just like just like this and once again let me shade it a little bit so that you can appreciate that this is a three-dimensional shape so draw the cone so you can shade it and we can even construct to the original so that well or we can construct this original shape so you see how it construct so it makes this the line that magenta line is going to do this type of thing it's going to go through the center of the base it's going to go through the center of the base just like that and our original shape our original right triangle if you just took a cross-section of it that included that included that line you would have your original shape I'm just an orange so the original shape is right is right over there so what do you get you get a cone where the radius of the base is three units interesting