Volume of a rectangular prism: word problem | Geometry | 6th grade | Khan Academy

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 6.46 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.