Formulas and units: Volume of a pool | Working with units | Algebra I | Khan Academy

We're told that Marvin has an inflatable wading pool in his backyard. 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 is kind of a small pool where you can just hang out a bit in it. You're not necessarily going to 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 4 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 centimeters. And if you multiply these two things, your actual units would not be cubic meters; it would end up with units of meter 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 want to re-express 60 centimeters in terms of meters. Well, how many meters is 60 centimeters? Well, a hundred centimeters make a meter, so I could write it this way: 100 centimeters equal one meter. Or another way you could think about it is one centimeter is equal to 0.01 of a meter. So 60 centimeters is going to be equal to 60 hundredths of a meter.

So now we can apply this because we're dealing with meters consistently now. So we can say, this is actually wrong. We could say the volume is going to be equal to the base in square meters — I'm going to write the units down to make sure we're doing the right thing — times the height times 60 over 100 meters.

And now everything works out. 4 times 60 over 100 is going to be 240 over 100, and then meter 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.