## Video transcript

human beings have always realized that certain things are longer than other things for exemplar this line section looks longer than this line section but that ‘s not so satisfy good to make that comparison you want to be able to measure you want to be able to quantify how much longer the second gear one is then the first one and how do we go about doing that well we define a unit duration we define a unit length so if we make this our unit length this we say this is one unit then we could say how many of those lengths are each of these lines so this first channel looks like it is we can do one of those units and then we could do it again so it looks like this is two units while this third one looks like we can get to see that ‘s one to three of the units so this is three of the units and right field here I ‘m just saying units sometimes we ‘ve we ‘ve made conventions to define a centimeter where the whole might look something like this and it ‘s going to look different depending on your screen door or we might have an inch that looks something like this or we have might have a foundation that I wo n’t be able to fit on this on the shield based on how big I ‘ve merely drawn the edge or meter so there ‘s unlike units that you could use to measure in terms of but now let ‘s think about more dimensions this is literally a one dimensional case this is 1d why is it one dimension well I can merely measure quantify I can only measure length but now let ‘s go to a 2d case lashkar-e-taiba ‘s go to two dimensions where objects could have a distance and a width or width and a height therefore let ‘s imagine two figures here that look like this so let ‘s say this is one of them this is one of them and notice it has a width and it has a stature or you could view it as a length in it or you could view it as a width and a length depending how you want to view it so let ‘s say this is one figure right over here and let ‘s say this is the early one so this is the other one correct over hera try to draw them reasonably well now once again now we ‘re in two dimensions and we want to say well how much how much in two dimensions quad is this taking up or how much area are each of these two taking up well once again we could good make a comparison this second if you viewed the miss carpets or rectangles the second rectangle is taking up more of my screen door than this first one but I want to be able to measure it so how would we measure it good once again we would define a unit of measurement hearty rather of fair a unit length we now have two dimensions we have to define a unit straight and so we might make our unit of measurement square and the unit square we will define as being a squarely where its width and its stature are both peer to the unit of measurement length so this is its width is one whole and its altitude is one unit and so we will frequently call this one square unit oftentimes you ‘ll say this is one unit and you put this two up here this literally means one whole squared and rather of writing unit I could have this could have been a centimeter so this would be one square centimeter but now we can use this to measure these areas and you say well how many just as we said how many of this unit of measurement length could fit on these lines we could say how many of these unit of measurement squares can fit in here and thus here we might take one of our units squared and say okay it fills up that much quad or we need more to cover all of it good there we ‘ll put another unit square there we ‘ll put another unit square right over there we ‘ll put another unit square right over there Wow for unit squares precisely cover this so we would say that this has an area of four four units four public square units or four units squared now what about this one right over here well here let ‘s see I could fit one two three four five six seven eight and nine therefore here I could fit nine nine units nine units squared lease ‘s keep going we have we live in a cubic world why restrict ourselves to only one or two so let ‘s go to the three-d font and once again when people say 3d they ‘re talking about three dimensions they ‘re talking about the different directions that you can measure things in here there ‘s only length here there ‘s duration and width Thor width and stature and here there will be width and stature and depth so once again if you have if you have let ‘s say a an object and now we ‘re in three dimensions where in the earth we live in that looks like this and then you have another object that looks like it looks like this that looks like this it looks like this moment object takes up more space more physical space than this first object does it looks like it has a larger volume but how do we actually measure that and remember volume is barely how much quad something takes up in three dimensions area is how a lot space something takes up in two dimensions duration is how much space something takes up in one dimensions but when we think about space we ‘re normally thinking about three dimensions thus how a lot space would you take up astir take up in the global that we live in indeed just like we did before we can define rather of a unit duration or unit of measurement area we can define a unit volume or a unit of measurement cube so let ‘s do that let ‘s define our whole block and here it ‘s a cube so all of its its length width and height are going to be the lapp value so my best undertake at drawing a cube and they ‘re all going to be one unit of measurement so it ‘s going to be one unit of measurement high one unit one unit thick and one unit one unit of measurement wide and sol to measure bulk because a well how many of these unit of measurement cubes can fit into these unlike shapes well this one correct over here and you wo n’t be able to actually see all of them I could basically break it down into sol let me see how well I can do this so that we can count them all it ‘s a little moment harder to see them all because you ‘re there ‘s some cubes that are behind us but if you think of it as two layers so one layer would look like this one layer is going to look like this so imagine two things like this stacked on crown of each other so this one ‘s going to have one two three four cubes now this is going to have two of these stacked on top of each other so hera you have eight unit cubes or you could have eight units cubed volume what about hera well if we try to fit it all in if we try to fit it all in let me see how well I could draw this well I can draw this it ‘s going to look something like this it ‘s going to look something like this obviously this is kind of a pugnacious draw and therefore if we were to try to take this apart you would basically have three you ‘d have a batch of three sections that will each look something like this my best attempt at drawing it three sections that would look look something like what I ‘m about to draw so it would look like this so three if you took three of these and stacked them on top of each other you would get this right over here and each of these have one two three four five six seven eight nine cubes in it nine times three you ‘re going to have twenty-seven twenty-seven cubic units in this one right over here thus hopefully that helps us think a little bite about how we measure things particularly how we measure unlike things in different number of dimensions specially in three dimensions when we call it volume

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