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

- 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.