The following formula estimates an average person's lung capac...

Question

The following formula estimates an average person's lung capacity V (in liters, where 1 L = 10³ cm³):

V = 4.1H ― 0.018A ―2.7 ,

where H and A are the person's height (in meters) and age (in years), respectively. In this formula, what are the units of the numbers 4.1, 0.018, and 2.7?

Accepted Answer

Hey, everyone in this problem, we're asked to assume that the equation to calculate a woman's blood volume. V in liters is V is equal to 0.3561 multiplied by H cubed plus 0.03308 multiplied by W plus 0.1833. OK. Where H is in meters, W as in kilograms and they represent the height and weight of the woman respectively. And we're asked to determine the units associated with the numbers in that equation. OK. So those three numbers in that equation, we're given four answer choices A through D and each of them contain different units or each of those three values. And we're gonna come back to those answer choices as we work through this problem. So let's start just by writing out our equation. So we have the volume is equal to 0.3561 H Cute. It was 0.03308 W was 0.1833. Hm. And we want to figure out the units on the right hand side. Now, on the left hand side, we have the volume V what we wanna do when we have a problem like this, we have the units on the left hand side, we have a bunch of things added on the right hand side together. We wanna recall the principle of homogeneity, right? So if we have the principal uh homo and Nanny tells us that the units for each term on the right hand side must match the units on the left hand side. OK? So the first term, 0.3561 HQ has to match with the units on the left. The second term, 0.03308 W has to match. And that final term that is just that number, 0.1833 also has to match. OK? So each of them individually has to match and when you add them all up, you're gonna have that same consistent unit. So let's start with that last term because it's just the number. OK? So we're gonna start with the last term. And what it tells us is that the units A V must be the same as the unit for that number. All we have there is that number. So that number has to be associated with the exact same units by our principle of homogeneity, which means that the units of 0.1833 is going to be liters and just like the volume on the left hand side, we take a look at our answer choices A B and D all have this answer. OK. So for 0.1833 it has the unit as a liter but answer C has it as a liter per kilogram. Ok. That's not correct. So we can eliminate option C now let's move to our next term. We're gonna go, let's just go with the middle term, we'll work our way backwards and the units of the, in this case must match the units of 0.03308 W OK. Well, the units are of V are in liters. The units of W are in kilograms. Hm. So what we essentially have here is that a leader has to equal some dimension or some unit of that number multiplied by a kilogram. So what that tells us is that the units of that number must be equal to a liter divided by a kilogram. OK. If we have liter divided by kilogram, we multiply it by kilogram, we're left with just liters. OK? In this case, I've used square bar. It's just to indicate that we're talking about the units but don't get mixed up. This does not indicate length. In this case, the L does indicate li OK. So we have liters per kilogram for that second value and let's just go back and highlight our leaders. So let's take a look at our answer choices. We are slowly narrowing them down. Option A and B are still in contention they have liters per kilogram for that second value. But option D has liters per meter cubed. OK. That is not correct. So we can eliminate option D and now we're left with that very first value and it's the last one we need to sort out in order to answer the question. OK. So we have the units of V again which are leaders after match the units of zero 0.3561 multiplied by Q. So what we get is that our leaders must be equal to whatever the unit associated with this number is 0.3561 multiplied by the unit associated with H cubes. We're told that the height is measured in meters. So we get meters cubed and this tells us that the units for this number 0.3561 must be liters per meter cubed. Maybe we can divide both sides by meters cubed just like we do with regular equations. And so our units are going to be liters per meter. Cute. And again, we can always double check this. OK? If we substitute this back into our equation, we have liters per meter cubed multiplied by meters cubed, the meters cubed will divide out. We're left with liters, right? And that's what we want. So back to our answer choices, we've now narrowed it down. We found that the units associated with the first number 0.3561 should be liters per meter cubed. The units associated with 0.03308 should be liters per kilogram and the units associated with 0.8 on 1833. Sorry are leaders. And so the correct answer here is option A thanks everyone for watching. I hope this video helped see you in the next one.

The following formula estimates an average person's lung capacity V (in liters, where 1 L = 10³ cm³):

V = 4.1H ― 0.018A ―2.7 ,
where H and A are the person's height (in meters) and age (in years), respectively. In this formula, what are the units of the numbers 4.1, 0.018, and 2.7?

Key Concepts

Units of Measurement

Dimensional Analysis

Coefficients in Formulas

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