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Formulas and units: Volume of a pool

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.

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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.