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Current time:0:00Total duration:3:30

Video transcript

so I have a three-dimensional solid right over here and I want to imagine what type of a shape I would get if I were to make a vertical cut and just to refresh ourselves or give our sense of us give us a sense of what a vertical cut is imagine if I if this was made out of jell-o or something kind of fairly soft but it's still a 3-dimensional solid and I were to make a cut let's say I were to make a cut right over here so let's say I have this big sharp metal thing let me draw it like that so you have this big sharp metal thing let me draw it a little bit neater so you have this big sharp metal thing that I'm going to cut right over here so this is the thing that I'm going to make the cut and I'm going to go straight down this is a vertical cut that we're talking about so this is the thing this is the thing that I'm going to cut with I don't make it big enough so that it can capture the shape that will result so this thing right over here it's right in front and I'm going to cut I'm going to make it go straight down and cut through this jello or whatever you want to call it this this trick this rectangular pyramid of jell-o and what would be the resulting shape of the intersection between the jello and this this thing that I'm using to cut it and now I encourage you to pause your video and think about what the resulting shape would be and the shape would be in two dimensions because this this purple surface is a two-dimensional it's a two-dimensional you could view this as part of a plane and so where this intersects when you cut down this rectangular pyramid is the shape we're looking for so I encourage you to pause the video and think about it or try to come up with it on your own so let's think about it and let me let me draw let me draw the rectangular perimeter again so that's the same one and now let me see what it would look like once I've done my cut once I've brought this thing down so then so then this is where I cut so I cut it right over here I cut it right over here and then it'll exit the bottom it'll it'll cut along this will cut along this side like that cut along that like that and then it will exit the bottom it'll exit the bottom right over there and so let me draw my whole thing and so once I slice it down it will look like this it will look like this my best shot at drawing it it will look like this this is a rectangular this is a so I should say this is a vertical cut so I brought this thing down and now the intersection between the thing that I'm cutting with and this this pyramid is going to be this shape right over here it cut into the top right over there it would get all the way to the bottom right over there and along this side it would cut right there and along that side it would cut right over there so what's the resulting shape in two dimensions of essentially the intersection between the slicer and end of the jello well it would be this thing it would look like a trapezoid let me do that in a new color i'm overusing i'm overusing that one color it would look it would look like a trapezoid so this would be the resulting shape so the resulting shape it doesn't so the resulting shape would look like this would look like this just like that if you made the cut right over there