Volume of rectangles inside rectangles

the uba's are moving from Houston to Egypt they pack their belongings in rectangular crates and hire a boxcar to ship the crates across land and sea the crates are made specifically to fit inside the boxcar with their bases facing down each crate has a base five metres long by 1.5 meters wide so let me draw that so each crate is five meters long and 1.5 meters wide 1.5 meters wide and has a height of 2 meters so tight might look something like this so it has a height of 2 meters so that's each of the crates and they're designed they're designed to fit inside a box car so this is a crate right over here do my best to draw a crate and they give us the dimensions of the boxcar a boxcar is 15 meters long so let me draw a boxcar here so it's 15 meters long maybe I'll try to make sure I can fit it on the page so this whole distance would be 5 meters and then another 5 meters here and then another 5 meters here so that would be 15 meters long so you could fit you could fit three of the crates along an edge like that three crates along an edge like that and then they tell us that it is three meters wide so this is 1.5 meters wide so you could put two of these to get you to 3 meters 3 meters wide let me draw this so we can see what's going on behind the scenes so you could go 3 meters wide for a boxcar and then it's 4 meters high so each of these are 2 meters high each of these are 2 meters so you could stack one up one more you can stack one more and so you have 2 meters plus 2 meters this entire distance this entire distance right over here is going to be 4 meters and I could draw the rest of the boxcar like this like this so there's a couple of ways to think about how many crates you could fit in a boxcar one way would be just the way that we're doing it right now we could visualize how many can you fit in this direction along the length how many can you fit along the width and how many can you fit along the height and you would have surely if we multiply those three numbers we would have counted the number of crates that could fit inside so you could fit one two three along the length so that'd be three you could fit two along the width 1.5 and 1.5 gets you to three meters so times two and then you could fit two along the height so times two gets us to three times two is six times two is twelve you can fit 12 crates in the boxcar now another way you could have done it is you could said okay we they're telling us that these are designed to fit so we really just have to compare the volumes how many times more is the volume of the box car than the crate I like doing it this way more just to make sure that the dimensions actually work out so that you can actually squeeze these in because the dimensions aren't right even if the even if the boxcar is twelve times the volume of one of the crates if the crates don't have the right dimensions you might not be able to squeeze exactly 12 crates in there but they're telling us that it is the exact dimension so we could figure out the dimensions of the boxcar then the dimensions of the crate and we can figure out how much larger the boxcar is how many times larger so the boxcar let's do the boxcar in this blue color the boxcar is 15 meters long 3 meters wide and 4 meters high so boxcar boxcar volume volume is equal to 15 and cubic meter so this 15 meters times 3 meters times 4 meters so this is going to be in cubic meters so this is going to be a c5 15 times 3 is 45 45 times 4 is 180 180 cubic meters cubic meters that's the boxcar volume and then what's the volume of the crate well the create volume create volume if we do our math right it should come out to 1/12 of this because that's what we just figured out is 5 times 1.5 times 2 so 5 times 1.5 times 2 well 1 point 5 times 2 is 3 times 5 is 15 so 15 cubic meters so how many times larger is the boxcar than the crate well what's 180 divided by 15 well it's exactly 12:10 times 15 is 150 and then 2 times 15 is 30 hundred 50 plus 30 is 180 so notice 180 divided by 15 is 12 so either way however you think about it I find this one to be a little bit easier to kind of just visualize the boxes you can fit 12 crates in the boxcar