Estimate how many books can be shelved in a college library with $3500 \textrm{ m}^2$ of floor space. Assume 8 shelves high, having books on both sides, with corridors 1.5 m wide. Assume books are about the size of this one, on average.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Here's a top down view of this library which we'll assume is square and we are told that we have corridors around each shelving unit of 1.5 meters and the area we are told is 3500 square meters. So if we imagine that this is a square then we can figure out the length of each wall here in this library; it's gonna be the square root of the area and that's gonna be 59.16 meters. And if we have a front-view of the shelf, this is the binding and it might say Giancoli or something or survey or whatever else and it's 4 centimeters wide if it's the same as the width of this textbook and if you look at it from the side, it looks like the book is about 20 meters depth so here is the binding here and this is the edge where you open it and while there's two of those on each side of the shelving unit so that's a total of 40 centimeters—width of the shelving unit—0.4 meters. So we have 1.5 meter width of the aisle, plus a 0.4 meters, width of the shelving unit so one aisle plus shelf is 1.5 plus 0.4 which is 1.9 meters so from the wall here to here is 1.9 meters. So we'll need to see how many of these 1.90 meter widths can we fit within this 59.16 meters. Now but before we do that, we'll figure out the length of a shelf; it's gonna be the length of the wall here minus the 1.5 meters plus 1.5 meters corridor space on each end. So we have 59.16 meters—length of the wall— minus 2 times 1.5 meters corridors that's 56.16 meters and so the number of books on a single shelf so that's just not a whole shelving unit but just a single shelf here going the full length of the unit would be would be this length of the shelf times 1 book for every 0.04 meters because a book is only 4 centimeters wide. So we have this maybe I should draw that so here's the front view of the whole shelving unit and it goes like this on and on and on more books, more books, 4 centimeters, 4 centimeters until you achieve a full shelving unit length of what did I say, 56.16 meters which is 59.16 minus 3 because we have 3 meter total length or total distance reserved for the corridor on each end. So we have 56.16 and then divide by 0.4 meters to see how many of these book widths can we fit within this length of the shelf and that's what's happening here. So 1404 books on a single shelf. Now this shelving unit is 8 shelves high and it has 2 sides so multiply this number of books on a single shelf by 8 and then multiply that result by 2 to get a total amount of books on a single shelving unit with both sides combined, 22464 books. And then ask how many shelving units can we fit within the library and the library has a 59.16 meter width so that's this width here and then divided by 1.9 meters for a shelving unit and corridor combined and I wrote that as one shelf plus aisle per 1.9 meters and the meters cancel leaving us with 31 shelving units and aisles. And so we have 22464 books per shelf aisle times 31 shelf aisles and shelf and aisle combined and that gives us about 7 times 10 to the 5 books can be stored in this whole library.