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Current time:0:00Total duration:3:20

CCSS.Math:

- [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.