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Volume of a rectangular prism: word problem

Mario has a fish tank shaped like a right rectangular prism. The tank is filled with marbles and water up to 6.4 cm. When the marbles are removed, the water level drops to 5.9 cm. The volume of water displaced by the marbles is found to be 56.16 cubic centimeters. Created by Sal Khan.

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Video transcript

- [Instructor] Mario has a fish tank that is a right rectangular prism with base 15.6 centimeters by 7.2 centimeters. So let's try to imagine that. So it's a right rectangular prism. This is a fish tank. Let me actually do it in blue. So it, one of the dimensions, that's not blue, that's orange. One of the dimensions is 15.6 centimeters. 15.6 centimeters. And then the other dimension of the base is 7.2 centimeters. 7.2 centimeters. So this is the base right over here. So let me draw this, try to put some perspective in there. And, of course, it is a right rectangular prism, this fish tank that Mario has. So it looks something like this. So this is his fish tank. Try to draw it as neatly as I can. So that's the top of the fish tank, just like that. I think this does a decent, respectable job of what this fish tank might look like. And let me erase this thing right over here. And there we go. There is Mario's fish tank. There is his fish tank, and we can even make it look like glass. There you go, that looks nice. All right, the bottom of the tank is filled with marbles. And the tank is then filled with water to a height of 6.4 centimeters. So the water is filled to a height of 6.4 centimeters. So this is the water when it's all filled up, 6.4 centimeters. So let's draw that. And I'll make the water, well, maybe I should have made it a little more blue than this, but this gives you the picture. So the height of the water right over here, actually, let me do that in a blue color. The height of the water right over here is 6.4, 6.4 centimeters. So that means that the distance from the bottom of the tank to the top of, not the tank, but to the top of the water, is 6.4 centimeters. 6.4 centimeters. Fair enough. So that's the top of the water. When the marbles were removed, and it started off with some marbles on the bottom. They don't tell us how many marbles. When the marbles are removed, the water level drops to a height of 5.9 centimeters. So when they're removed, the water level drops by a little bit, to 5.9 centimeters. 5.9 centimeters. So it drops. It drops to 5., it drops to 5.9, from 6.4 to 5.9 centimeters. What is the volume of the water displaced by the marbles? So when you took the marbles out, the water dropped from 6.4. So it dropped from 6.4 centimeters down to 5.9 centimeters. 5.9 centimeters. So how much did it drop? Well, it dropped .5 centimeters, So it dropped, it dropped 0.5 centimeters. So what does that tell us about the volume of water displaced by the marbles? Well, the volume of water displaced by the marbles must be the amount of the, must be equivalent to this volume. This volume of this, I guess this, I guess this is another rectangular prism that is the same, where the top area is the same as the base of this water tank. And then the height is the height of the water drop. When you put the marbles in, it takes up more volume, it pushes the water up by that amount, by that volume. When you take it out, then that volume gets replaced with the water down here, and then that volume goes back down, the water level goes down to 5.9 centimeters. So we're essentially trying to find the volume of a rectangular prism that is, that is equal to, so it's gonna be 15.6 by 7.2 by .5. And I haven't drawn it to scale yet, but I wanna see all of the measurements. So it's going to be 15.6 centimeters in this direction, it's going to be 7.2 centimeters in this direction, and it's going to be .5 centimeters high, 0.5 centimeters high. So we know how to find volume, we just multiply the length times the width times the height. So the volume in centimeter cubed, and we're (indistinct) scale, we're multiplying centimeters, times centimeters, times centimeters, so it's gonna be centimeters cubed, is going to be, so lemme write this down. The volume is going to be 15.6 times 7.2 times 0.5, and it's gonna be in centimeters cubed, or cubic centimeters, I guess we could call them. Well, let's first multiply 7.2 times 0.5. We can do that in our head. This part right over here is going to be 3.6, essentially just half of 7.2. So then this becomes 15.6 times 3.6. So let me just multiply that over here. So 15.6 times 3.6. So I'll ignore the decimals for a second. 6 times 6 is 36, 5 times 6 is 30, plus 3, is 33. 1 times 6 is 6, plus 3, is 9. And then let's place a zero here. We're down in the 1s place, but I'm ignoring the decimals for now. 3 times 6 is 18, 3 times 5 is 15, plus one is 16, 3 times 1 is 3, plus 1 is four. And then we get 6, 3 plus 8 is 11, 16, 5. Now, if this was 156 times 36, this would be 5,616, but it's not. We have two numbers to the right of the decimal point, one, two, so it's going to be 56.16. So the volume, the volume, and we deserve a drum roll now, is 56.16 cubic, cubic centimeters.