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Perimeter, area, and volume | Worked example

Sal Khan works through a question on volume from the Praxis Core Math test.

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Video transcript

- [Narrator] Pavel's new aquarium is forty-eight inches long, sixteen inches wide, and twenty-four inches tall. If Pavel wants to fill one-sixth of the aquarium with sand, how many cubic inches of sand does he need? Pause this video and see if you can figure this out. Okay, now let's draw this aquarium. It is forty-eight inches long. So let me draw that like this. So, it is forty-eight inches long and they tell us it is sixteen inches wide. So I'll draw it like that. So it is sixteen inches wide and I can also draw that other here, that would essentially be the base of the aquarium. So that's the base of the aquarium and actually think about how tall it is and it's twenty-four inches tall. Do that in orange. Twenty-four inches tall so, it might look something like this. So, it is twenty-four inches tall. So, that height right over there is twenty-four. So that is, I could draw a straighter line than that. That is twenty-four and that is twenty-four and then I can connect them. We know that this is forty-eight, this is forty-eight and we know that this is sixteen inches. I've taken some care to make it color coated. So there is two ways that we could try to approach this, we could just figure out the volume of the entire aquarium and just think about well what is one-sixth of that volume. Or another way to think about it if Pavel is filling it one-sixth of the aquarium with sand the sands going to go one-sixth up the height. So how tall would that be? What's one-sixth of twenty-four inches? So what would this height be? That it gets that the sand would go up in the aquarium. Well, if we say so this is going, this height right over here, let me do that in a deeper color. So this height of the sand is going to be one-sixth of twenty-four inches. So one-sixth times twenty-four. Well one-sixth times twenty-four is the same thing as twenty-four divided by six, so this height right over here is going to be four inches. And so if you want to think about the cubic inches of sand we just think about the volume of this rectangle right over here. Which, is going to be, forty-eight inches wide times sixteen or forty-eight inches long times sixteen inches wide times four inches high. Times four inches Which, is going to be equal to, you could do that, try to do that in your head or on paper. But you could also use a calculator of course. And so we are going to get forty-eight times sixteen times four is equal to three thousand seventy two cubic inches. Three thousand seventy two cubic inches. So you could write that as inches cubed or cubic, or you could write it out as, sometimes you will see it, either way cubic, cubic inches. And we're done.