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## Appropriate units

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# Appropriate units

## Video transcript

- [Instructor] Luiza runs
a lawn-mowing business. She decides to measure the rate at which the volume of fuel she uses increases with the area of the lawn. What would be an appropriate
unit for Luiza's purpose? So let me reread this to
make sure I understand it. She decides to measure. She's gonna measure the rate at which the volume of fuel she uses increases with the area of the lawn. So her unit should be something
that says volume per area. She wants to see how her
volume of fuel increases with the area of the lawn. So it should be volume per
area, should be her rate. So let's think about which of these units give us volume per area. So liters right over here,
that is definitely volume but this right over here
isn't area, this is distance. If it said square kilometers
or kilometers squared then we'd be in business. So we could rule this one out. Centimeters per kilometer. Well, this is a distance per
distance, not a volume per area so we can rule that out. Centimeters per square kilometers. Well, this is a distance per area or distance per distance squared but that is not volume per area. So let's rule that one out. Now, liters per kilometer squared. This one's looking good. This is a volume in liters and this right over here is an area and this isn't the only
one that would have worked but this is out of the choices, this is the only one that works. If they gave, if it was something like a pint per foot squared
or a pint per square foot or even if it was meter
cubed per kilometers squared, that would have also been volume per area but this is the best choice of these. Let's do another one of these. Snow is piling outside Cameron's house. He decides to measure the
rate at which the height, the height of the pile
increases over time. What would be an appropriate
unit for Cameron's purposes? And like always, pause the video and see if you can figure
it out on your own. So the rate at which
height increases over time. So it should be a height per time or really I should say a distance per time is what the height is going to be doing, the rate at which the height
is changing over time. It should be a distance or
maybe even better, a length. Length per unit time. So let's see, this is hours per meter. So this is time per length. This is the reciprocal of that. This one right over here,
this is time per length as opposed to length per time
so I would rule that one out. Liters per minute. This is a volume per unit time, not a length per unit of time. Rule that one out. Minutes per liter. This is a time per volume. Well, we don't wanna do a time per volume. We want a length per time. Meters, that's a length per time, hour. That one works. Meters per hour. This is a length and that is a time. And it's good to always go
back to the original context. He decides to measure the rate at which the height of the
pile increases over time. So if someone said, hey, that height of that pile
is increasing five meters. Well, that would be too much for snow but let's say it's increasing
half a meter per hour which even that would be quite fast but half a meter per hour. That makes sense in your brain. Hey, every hour I'm gonna get
half a meter more of snow. If someone were to tell you, hey, the snow outside is
increasing at a rate of five hours, is increasing at a rate of
say five liters per minute, well, that right there, that could be maybe the volume of snow maybe over your entire lawn or something but that would not be giving
you the height per time. Height per time would
be the length per time. Right over here.