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## Geometry 222-226

### Course: Geometry 222-226 > Unit 1

Lesson 7: Volume and surface area word problems# Volume of rectangles inside rectangles

CCSS.Math:

How many crates can we fit into a boxcar? We'll explain that there's more than one way to solve for the volume in this problem. Created by Sal Khan.

## Want to join the conversation?

- How do u find the surface area of a triangular prism?(29 votes)
- Alot of these answers are giving you the volume, which is how much fits inside a triangular prism, but not the surface area, which is how big the surface is - like if you had to wrap it with wrapping paper, how much paper would you need? I break it down into the same shapes so I know what I've calculated already and don't forget a side. First I take the (Width of the base * Height of the tallest point) for the triangle side, then I +add it to the (Length of the base * Width of the base) for the bottom side, then I +add it to the (Length of the base * Height of the tallest point) for the other side that is not the longest side of triangle side, then I +add it to the (Length of the base * Side that is the hypotenuse (longest side of triangle)). In math, that is SA = wh + Lw + Lh + Ls which will always be the unit of measurement^2, since it is an area and not how long around something is and not a volume.(11 votes)

- The question is about The Ubas moving from Houston to Egypt, but why do the crates say "china shipping."(11 votes)
- Haha the picture is of a port. Hence Cargoes could travel(2 votes)

- At2:38Sal wrote 12 after describing the volume of a box instead of 12 to the third.(5 votes)
- In this case he's counting the number of crates that can fit in the boxcar. If he had wanted to get the volume of the crates, he would have said 12 cubic meters (meters to the third), not 12 to the third.(12 votes)

- Anybody know the question said something about Houston to Egypt but the picture shows "China Shipping"(5 votes)
- Well 1.) China makes crates in bulk, so they could have purchased the crates for cheaper from China Shipping. 2.) The crates would have to travel across the ocean to get from the good old state of Texas to Egypt, so China might have gotten some jumbo-crates to stuff the smaller crates from the boxcar inside. 3.) It was probably just an attempt to make the screen and problem seem more interesting, but Sal overlooked that detail. It might have been too much trouble to find something that specific. *\
*(^-^)*/* idk for sure though...(7 votes)

- how would you find the area with only the height(6 votes)
- How do you find the volume of a pyramid inside a rectangle?(4 votes)
- how do you find the surface area of a rectangular prism(4 votes)
- SA=2(wl+hl+hw)(3 votes)

- I NEED HELP WITH THIS PROBLEM!

The volume of rectangular prism is same as: The

Volume of cuboid, Volume of cube, Volume of cone or None of these(2 votes)- Hi, Daniel.

First don't stress out and think it through. The formula to solve for the volume of a rectangular prism is V=lwh. Since a square is just a fancy rectangle you can use the same formula for both. This also goes for volume. A cube is just a fancy rectangular prism. I hope this helps and that should be the answer.

P.S. I am not a teacher. I am just a friendly, weird teen who LOVES math and also LOVES helping others succeed. :)(2 votes)

- where did you get the problem? just asking(2 votes)
- Math Teacher or in the case, A Khan Academy Skill you are practicing. (Hope I Helped!)

:-)(1 vote)

- what if the container was a slope and not a rectangular prisim?(2 votes)

## Video transcript

The Ubas are moving
from Houston to Egypt. They pack their belongings
in rectangular crates and hire a boxcar to ship the
crates across land and sea. The crates are made specifically
to fit inside the boxcar with their bases facing down. Each crate has a base 5 meters
long by 1.5 meters wide. So let me draw that. So crate is 5 meters
long, and 1.5 meters wide, and has a height of 2 meters. So its height might look
something like this. So it has a height of 2 meters. So that's each of the crates. And they're designed
to fit inside a boxcar. So this is a crate
right over here. I'll do my best to draw a crate. And they give us the
dimensions of the boxcar. A boxcar is 15 meters long. So let me draw a boxcar here. So it's 15 meters long. Maybe I'll try to make sure
I can fit it on the page. So that this whole
distance would be 5 meters, and then another 5 meters here,
and then another 5 meters here. So that would be 15 meters long. So you could fit three of the
crates along an edge like that. And then, they tell us
that it is 3 meters wide. So this is 1.5 meters wide. So you could put two of
these to get you to 3 meters. Let me draw this so
we can see what's going on behind the scenes. So you could go 3 meters
wide for a boxcar, and then it is 4 meters high. So each of these
are 2 meters high. So you could stack one more. And so you have 2
meters plus 2 meters. This entire distance right over
here is going to be 4 meters. And I could draw the rest
of the boxcar like this. So there's a couple of ways to
think about how many crates you could fit in a boxcar. One way would be just the way
that we're doing it right now. We could visualize. How many can you fit in this
direction along the length? How many can you
fit along the width? And how many can you
fit along the height? And essentially, if we
multiply those three numbers, we would have counted
the number of crates that could fit inside. So you could fit 1,
2, 3 along the length. So that'd be 3. You could fit 2 along the width. 1.5 and 1.5 gets you to
3 meters, so times 2. And then you could fit 2
along the height, so times 2, gets us to 3 times 2
is 6 times 2 is 12. You can fit 12
crates in the boxcar. Now, another way you could have
done it is you could say, OK, they're telling us that
these are designed to fit. So we really just have
to compare the volumes. How many times
more is the volume of the box car than the crate? I like doing it
this way more, just to make sure that the
dimensions actually work out, so that you could
actually squeeze these in. Because if the
dimensions aren't right, even if the boxcar is 12
times the volume of one of the crates, if
the crates don't have the right
dimensions, you might not be able to squeeze exactly
12 crates in there. But they're telling us that
it is the exact dimensions. So we could figure out the
dimensions of the boxcar, then the dimensions of the crate. And then we could figure out
how much larger the boxcar is, how many times larger. Let's do the boxcar
in this blue color. The boxcar is 15 meters long, 3
meters wide, and 4 meters high. So boxcar volume is equal
to 15 in cubic meters. So there's 15 meters times
3 meters times 4 meters. So this is going to
be in cubic meters. So this is going to be--
let's see, 15 times 3 is 45. 45 times 4 is 180 cubic meters. That's the boxcar volume. And then what's the
volume of the crate? Well, the crate volume--
if we do our math right, it should come out
to 1/12 of this, because that's what
we just figured out, is 5 times 1.5 times 2. So 5 times 1.5 times 2. Well, 1.5 times 2 is 3, times
5 is 15, so 15 cubic meters. So how many times larger is
the boxcar than the crate? Well, what's 180 divided by 15? Well, it's exactly 12. 10 times 15 is 150. And then 2 times 15 is 30. 150 plus 30 is 180. So notice, 180
divided by 15 is 12. So either way, however
you think about it-- I find this one to be a
little bit easier to kind of just visualize
the boxes-- you can fit 12 crates in the boxcar.