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Current time:0:00Total duration:3:19

so these are two pictures of the same figure this is a front view of the object and this is the back view of the object and if a unit cube looks like this what I want to do is I want to figure out the volume of this figure in terms of unit cubes or in terms of cubic units and encourage you to pause the video and think of it on your own before we we try it together all right well there's a bunch of ways that we could tackle this all of them kind of breaking this figure up in different ways one way we could do it we could break it up into this I guess we could call it a rectangular prism so if you could see through there would be like this so this piece right over here this piece right over here and I'll redraw it here so you can visualize it so if I were to redraw it it looks like this it looks like this and what are its what are its dimensions well it's four four units wide it's two units high and then it's four units we could say long or four units deep so just like that and so what's the volume of this yellow part well the volume is just you multiply these three dimensions the length times the width times the height so the volume is going to be our length times our width times our height four times four is 16 times 2 is 32 but we're not done that's just the volume of this yellow part we still have to take into consideration the volume of this piece right over here that we haven't figured out yet this piece right over there and this one might just jump out at you you could just count the unit cubes but I'll redraw it here just to show you what's going on all right so it looks like this it looks like this and what are its dimensions well it's too wide too high and we could say 1 deep or 1 long and so it's volume is going to be equal to your length or I could say well your length times your width times your height which is equal to four and you just see that there's one two three four unit cubes in this object so the total volume is going to be 32 plus 32 plus 4 is equal to 36 now of course there's other ways to tackle it you could just say hey let's figure out the volume of the blue layer and then just double it because that red layer has the same volume as the blue layer and the blue layer you could say well like it's only one deep so we just have to count the cubes up here and then we'll know how many unit cubes fit into it so you literally could just count one two let me do it a color you could actually see you just have to go 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 so you see there are 18 cubes in the blue layer and then there's another going there going to be another 18 in the red layer plus 18 that also gets you to 36 unit cubes or a volume of 36 cubic units