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## Algebra (all content)

### Course: Algebra (all content)ย >ย Unit 15

Lesson 2: Appropriate units# Formulas and units: Volume of a pool

CCSS.Math:

When using formulas to calculate real-world quantities, we need to make sure our units are consistent. In this video, the base area of a pool is given in square meters while its height is given in centimeters. In order to use the formula for volume, we need to convert one of the measurements to units that match the other measurement.

## Want to join the conversation?

- Sal, how did you get s^3 at2:32? This area was unclear for me.(11 votes)
- He got s^3, because s^2 is s*s, so if you multiply another s it will simplify to s^3(21 votes)

- I thought when you divide by something, you multiply by the reciprocal. when you divided by the seconds, why did you multiply by 1/s instead of the reciprocal s/1?(11 votes)
- The reciprocal of
`s/1`

IS`1/s`

. So, I'm not sure what you mean.(4 votes)

- why did you divide by seconds?(3 votes)
- Instead of writing Joules / s, we write

kg*m^2 / s^2 / s

because kg*m^2 / s^2 = Joules.

Hope this helps!(5 votes)

- 2:12Why is dividing by seconds the same as multiplying 1/s?(3 votes)
- Because dividing is the same as multiplying by the reciprocal.(1 vote)

- The following equation is not from this video but it is same type of problem:

Consider V=IR where I=A and R=kg*m^2/s^3*A^2

(V=A times Kg times m squared divided by (or over) s cubed times A squared)

A(kg*m^2/s^3*A^2)

The answer seems to be Kg*m^2/s^3*A

My question is why does the variable A in the final answer left with no exponents?(2 votes)- That is because:

A/Aยฒ = 1/A

Technically you could see the "A" in the denominator having an exponent of 1, but standard convention is to omit the exponent if it is 1. Comment if you have questions.(5 votes)

- I am sure I am confusing myself, but at1:09, Sal says that the volume of a cylinder is b * h. According to Google, the volume of a cylinder is another formula, not the one he mentioned. So what does Sal mean by that?

Fellow Khan Academy User(1 vote)- Sal's formula assumes you already know the area of the base. The area of the base time height will give you the volume of the cylinder. However, you likely won't know the base, so the more commonly used formula is: Area = (Pi R^2)h

The Pi R^2 calculates the area of the base.

Hope this helps.(5 votes)

- Is saying .6 m is = 60cm? Just curious(2 votes)
- That is correct, metric system allows you to move the decimal, and m to cm (smaller units require bigger numbers) requires decimal move two places to the right.(2 votes)

- In mathematics, the caret symbol (^) represents an exponent. For example, 2^2 is equal to 4.(2 votes)

- is there a video that explains like cm meters cubic whatever he is talking about just to know because I am very confused. you know volume and stuff(2 votes)
- Cubic meters is just m x m x m it is also the volume of a cube with side length 1 meter.(1 vote)

- Starting at2:06, Khan talks about how dividing by s gives you kg*m^2/s^2 * 1/s^2. What I'm confused about is the s. I get that you have to flip the fraction and multiply it when dividing, leading you to align s^2 and s^1 to get s^3. However, in an expression like x^8/x^5, you end up having x^3 due to the properties of exponents. So could someone clarify why we wouldn't subtract the powers of S in this case? Thanks(1 vote)
- I do not know if this helps, but with x^8/x^5, you have a variable x on top and bottom. With the units of (km*m^2/s^2)/s, you have the s on the bottom of the numerator and on top of the denominator, so when you flip by dividing, they both end up on bottom, thus the exponent rule you use is adding because they would both now be in the denominator.(3 votes)

## Video transcript

- [Instructor] We're told that Marvin has an inflatable wading
pool in his back yard. The pool is cylindrical with a base area of four square meters and
a height of 60 centimeters. What is the volume of
the pool in cubic meters? Pause this video and see
if you can figure that out. All right, now let's work
through this together. And let's just first visualize what this cylindrical
wading pool would look like. It would look something like this. A wading pool's kind of a small pool where you can just hang out a bit in it. You're not necessarily gonna
swim around too much in it. So it might look something like this. I know I'm not drawing it perfectly. It's kind of a hand-drawn situation, and I'm making it transparent
so that we can see the base. So the wading pool would
look something like that. They tell us that we have a
base area of four square meters. So this area right over
here, that's the base. That is four square meters. And it has a height of 60 centimeters, tell us that right over there. So this height is 60 centimeters. So the volume, our
reaction might be to say, "Okay, the volume of a cylinder
is the area of the base times the height." And so in this case, why wouldn't we just take four times 60, times 60, and we would
get a volume of 240. And we want it in cubic meters, so we just say 240 cubic meters. Is this true? Did I just do this correctly? Well, some of you might have realized that what I just multiplied, I didn't multiply four square meters times 60 meters to get 240 cubic meters. I just multiplied four square meters times 60, 60 centimeters. And if you multiply these two things, your actual units would
not be cubic meters. You would end up of units of
meters squared centimeters, which is not what they want and that is kind of a
bizarre set of units. So in order to get the
answer in cubic meters, we would wanna re-express 60
centimeters in terms of meters. Well, how many meters is 60 centimeters? Well, 100 centimeters make a meter. So I could write it this way. So 100 centimeters equal one meter. Or another way you could think about it is one centimeter is equal
to 1/100 of a meter. And so 60 centimeters is going to be equal to 60/100 of a meter. So now we can apply this, 'cause we're dealing with
meters consistently now. So we can say, so this is actually wrong. We could say the volume
is going to be equal to the base in square meters, and I'm gonna write the units down and make sure we're doing the right thing, times the height, times
60 over 100 meters. And now everything works out. Four times 60 over 100 is
going to be 240 over 100. And then meters squared times meter, we are left with cubic meters, which is exactly what they asked us for. And of course, we could rewrite
this as 2.4 cubic meters. And we are done.