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# How volume changes from changing dimensions

## Video transcript

so I have a rectangular prism here we're given two of the dimensions the width is two the depth is three and this height here we're just representing with an H and what we're going to do in this video is think about how does the volume of this rectangular prism change as we change the height so let's make a little table here so let me make my table so this is going to be our height and this is going to be our volume V for volume and so let's say that the height is five what is the volume going to be pause this video and see if you can figure it out well the volume is just going to be the base times height times depth or you could say it's going to be the area of the square so it's the width times the depth which is six times the height so that would be 2 times 3 times 5 so 2 times 3 times 5 which is equal to 6 times 5 which is equal to 30 30 cubic units we're assuming that these are given in some units so this would be the units cubed all right now let's think about it if we were to double the height what is going to happen to our volume so if we double the height our height is 10 what is the volume pause this video and see if you can figure it out well in this situation we're still going to have 2 times 3 2 times 3 times our new height times 10 so now it's going to be 6 times 10 which is equal to 60 notice when we doubled the height if we just double one dimension we are going to double the volume let's see if that holds up let's double it again so what happens when our height is 20 units well here our volume is still going to be 2 times 3 times 22 times 3 times 20 which is equal to 6 times 20 which is equal to 120 so once again if you double one of the dimensions in this case the height it doubles it double the volume and you could think of it the other way if you were to have if you were to go from 20 to 10 so if you have one of the dimensions it has the volume you go from 120 to 60 now let's think about something interesting let's think about what happens if we double two of the dimensions so let's say so we know I'll just draw these really fast we know that if we have a situation where we have two by three and this height is five we know the volume here is thirty thirty cubic units but now let's double two of the dimensions let's make this into a ten and let's make this into a four so it's going to look like this and then this is going to be a four this is still going to be a three and our height is going to be a ten so it's going to look something like this so our height is going to be a ten I haven't drawn it perfectly to scale but hopefully you get the idea so this is our height at ten what is the volume I'm going to be now pause this video and see if you can figure it out well four times three is 12 times 10 is 120 so notice when we doubled two of the dimensions we actually quadrupled we actually quadrupled our total volume think about possibly to think about why did that happen well if you double one dimension you double the volume but here we're doubling one dimension and then another dimension so you're multiplying by two twice so think about what would happen if we doubled all of the dimensions how much would that increase the volume pause the video and see if you can do that on your own in general if you double all the dimensions what does it do to the volume or if you have all of the dimensions what does that do to the volume