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# How many footballs would fit in Levi’s® Stadium?

Eric Reid asks Sal Khan about how many footballs it would take to fill Levi's® Stadium.

*This content is provided by the 49ers Museum Education Program.*.## Want to join the conversation?

- how many footballs would fit the earth?(1 vote)
- football stadiums are really big i wonder if anybody actually measured how many footballs will go in there(1 vote)

## Video transcript

- Hey, Sal, how many footballs
do you think will fit in Levi's Stadium? - [Voiceover] That's a
great question, Erik, and I'm going to tackle
it by trying to estimate what the volume of the stadium
is and then think about what the volume of a football is and then think about how
much larger the volume of a stadium is than a football. And then we're gonna make some adjustments knowing that we can't
perfectly pack the footballs in and that the volume of a
stadium isn't just filled with free space. It has seats, it has
stuff behind the seats where fans walk in and buy
their sodas and whatever else. And so we're gonna make
some assumptions there. So let's just start with the
volume of the stadium itself. And the dimensions of
the stadium, lengthwise. So, if we look at this
dimension right over there. That is approximately,
and I'm going to do it all in approximations, this
is not going to be exact, that's approximately 1,000 feet. 1,000 feet. Now, if you look at the
width of the stadium. So if you were to say
roughly from there to there, so this is going now across the stadium, that is, you all gave the
number of 762 feet to me, so I'll go with, I'll just
use that number actually. 762 feet is the width. And then the height of
the stadium is 207 feet. And I'm not sure which point,
maybe that's the highest point of the stadium, let me
at least write that down. Once again, this is all an approximation. Just to get a sense of how
many footballs can fit in this. And I have a feeling
it's going to be a lot. So the height of the stadium,
that's going to be 207 feet. So if you had a rectangular
prism with those dimensions, and actually the length,
the exact dimensions you all gave me was 1,014 feet. So if you had a rectangular
prism with these dimensions where it was 1,014 feet long,
so let me write that down. 1,014 feet long, 762 feet
wide, and 207 feet high, it's pretty straight forward
to figure out the volume there. So that's 207 and let
me just finish drawing the rectangular prism so
that we can visualize it. So, it would look like that. We could figure out the volume
there just by multiplying the length times the
width times the height. So let's to that. Let me get a calculator out. So the length is 1,014
times the width is 762 times the height which is 207
gets us to about 160 million. And I'm going to start dealing
with approximations here because this isn't going
to be very precise. 160 million and our dimensions here are feet times feet times feet. So 160 million cubic feet. So the volume of a
rectangular prism like this is going to be approximately
160 million cubic feet. Now let's think about what
the volume of a football is. And I did a little bit
of work ahead of time and the volume of a football, I was able to find it in inches, once again this is an approximation, so football volume is
approximately 460 cubic inches. So I could write that as inches cubed. Now that might seem a
lot until we think about how many cubic inches are
actually in a cubic foot. So a cubic foot is going to, of course, be 12 inches by 12 inches by 12 inches. Let me make sure it looks like a cube. Alright, so that's our cubic foot there. At any time, I encourage
viewers, people watching this to pause the video and try
to figure out pieces of this. So, if you have 12 inches
by 12 inches by 12 inches how many cubic inches can
you put in a cubic foot? Well, we could do that in our
head but for the sake of time I'll say that's going to
be 12 to the third power or 12 cubed. That's what they call it, cubed. Because that's how you figure
out the volume of a cube. 12 to the third power. There's 1,728 cubic inches per cubic foot. So, 1,728 inches cubed per foot cubed. So how many cubic feet
is 460 cubic inches? Well, that's going to be whatever
fraction 460 is of 1,728. So, let me figure that out. So, if I have 460 divided by
1,728 we get to about 0.27. So the volume of a football in cubic feet, and this might make a little
bit more intuitive sense, the football volume is going to be approximately 0.27 cubic feet. There's a lot of cubic
inches in a cubic foot. So this is a little less
than a third of a cubic foot. And that makes sense with our intuition. When we hold a football it
looks less than a cubic foot. It's a little less than a third
of a volume of a cubic foot. So now, if we assume the
stadium was just a big empty rectangular prism with the
volume of 160 million cubic feet and the volume of a football
is a little under a third of a cubic foot, then
we could just divide. Let me get my calculator out again. So, this is all going to
be, it's a rough number. 160, let's see, that's
160,000, one two three, that's 160 million. That's the volume of just this
abstracted simplified stadium and then we're gonna divide
it by our approximate volume of a football in cubic feet
and we get pretty close, this is an interesting number,
pretty close to 600 million. So about 590 million. So, approximately 590 million footballs, if you were perfectly able
to fit them in without any extra space or anything,
could fit into this rectangular prism which we used
to approximate the stadium. Now I would say that
this is a high number. This is an upper bound. Because when you put
the footballs in there, they're not going to fit in perfectly. There's going to be all this empty space. So if you have a football
there, that's my best attempt at drawing, I could draw a
football better than that. I should really draw it in
a football color as well. So if you have a football
there, and it was next to another football right over
there, and that was next to another football right over there. And I'm drawing it in two dimensions. Obviously if we're packing the stadium, it's going to be in three dimensions. There's a whole bunch of empty space here. Let me get this in a
color that you can see. There's a whole bunch of empty
space between the footballs. And we're just seeing that
empty space in terms of two dimensions. It actually will seem
like even more volume when you can think about
it in three dimensions. So let's say that that
wastes 20% of the space. So, you're only gonna be
able to get 80% of the volume is going to actually be
filled up with footballs. And so I can multiply that
by 80%, let me do that. So times .8, that gets us to
about 474 million footballs. And then I would adjust it
again because once again we assumed that the
stadium was just this empty rectangular prism, it clearly isn't. There's all sorts of things here. There's bleachers, there's
all of this kind of the building part below the bleachers that seems that it would take up at least, you know I'm just eyeballing
it here, looking at this. We could do a more exact approximation maybe in a future video. But I would say that's taking
up at least 25% of the volume of the actual stadium. So, let's just say that
75% is actually there to be filled up. So let's multiply this
by another 75%, or by .75 and we get about 355 million footballs. So that's the number I'll go with. So I'll say approximately
355 million footballs. Which is a lot of footballs. And I didn't even consider
you could actually fill up all of the empty
space in the building part of the stadium with footballs as well, so maybe you can get a few more in there. But it's definitely going
to be in the hundreds of millions of footballs. Really good questions, Erik.