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## 6th grade

### Course: 6th grade > Unit 10

Lesson 3: Volume with fractions- Volume of a rectangular prism: fractional dimensions
- Volume by multiplying area of base times height
- Volume with fractions
- How volume changes from changing dimensions
- Volume of a rectangular prism: word problem
- Volume word problems: fractions & decimals

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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.

## Want to join the conversation?

- At3:40I did not understand what he meant(23 votes)
- he means the marbles took up some water capacity and made it 6.4cm than when took out 5.9cm(0 votes)

- What is a right-rectangular prism, and what's the difference between right-rectangular prism and a rectangular prism?(23 votes)
- How would i find out the surface areas of various prisms?(15 votes)
- add all of the area of each face @Daniel Kim(4 votes)

- How many 0.5 cm x 0.5 cm x 0.5 cm cubes are needed to completely fill a rectangular prism measuring 4 cm x 3 cm x 3 cm?(8 votes)
**volume of unit cube**= 0.5 cm x 0.5 cm x 0.5 cm

= 0.125 cm^3

**volume of prism**= 4 cm x 3 cm x 3 cm

= 36 cm^3

how many cubes are needed to fill = 36/0.125

= 288

Therefore, 288**cubes**are needed to completely fill a

rectangular prism measuring 4 cm x 3 cm x 3 cm.(15 votes)

- What is the mathematical definition of a prism?(8 votes)
- This is from Google.'' A solid object with two identical ends and flat sides: • The sides are parallelograms (4-sided shape with opposites sides parallel) • The cross section is the same all along its length. The shape of the ends give the prism a name, such as "triangular prism" It is also a polyhedron.''(11 votes)

- I have 2 questions. 1. Why does the official name "VOLUME" named for sound. 2. Isn't Volume basically finding area of a 3D Shape?(6 votes)
- It's cubic because volume occupies a three dimensional space.(6 votes)

- Can we time it by base x height x wight and the decimal as the height(7 votes)
- No, actually the base is the length and width. So it would be base x height.(6 votes)

- does the shape of the rectangle have something to do with the anwser.(8 votes)
- no, the volom of the mavels will be the same in a fish tank or the sea.(4 votes)

- Again, why are all these videos so old?!(8 votes)
- Do you have an issue with that?(1 vote)

- wait why is it cubed cenimeters?(4 votes)
- Because the question is talking about volume (so that is 3 dimensions or cubed, length*width*height). If we are talking about area that is 2 dimensions or squared (length*width) & if we're talking about one dimension well that is just one measurement (like length of a line segment). Hope that helps!(8 votes)

## Video transcript

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. Since it's a fish tank, let
me actually do it in blue. That's not blue, that's orange. One of the dimensions
is 15.6 centimeters. And then the other dimension
of the base is 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. And that's 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 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 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. Fair enough. So that's the top of the water. When the marbles are
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. 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. So how much did it drop? Well, 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 equivalent to
this volume of this-- I guess this is another
rectangular prism. That is, 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 water, 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 equal to-- so it's going
to be 15.6 by 7.2 by 0.5. And I haven't drawn
it to scale yet, but I wanted to see
all 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
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. We're multiplying centimeters
times centimeters times centimeters. So it's going to be
centimeters cubed. So let me write this down. The volume is going to be
15.6 times 7.2 times 0.5, and it's going to 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 0 here. We're down in the
ones place, but I'm ignoring the decimals for now. 3 times 6 is 18. 3 times 5 is 15, plus 1 is 16. 3 times 1 is 3, plus 1 is 4. 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-- and we
deserve a drum roll now-- is 56.16 cubic centimeters.