Question

Estimate how many books can be shelved in a college library with 3500 m2 of floor space. Assume 8 shelves high, having books on both sides, with corridors 1.5 m wide. Assume books are approximately 25 cm deep and 5 cm wide, on average.

Answer 1

Answer:

This college library would hold approximately $6*10^{5}/tex] books.Step-by-step explanation:Having books on both sides, and each book being 25 centimeters (there is 100 cm in a meter, so 25 cm=0.25 m) deep, shelves must be around 50 cm (or 0.5 m) wide.If corridors must be 1,5 m wide, every two linear meters (perpendicular to corridors and shelves) of floor space there is 1.5 m of corridors and 0.5 m of shelves and that sequence repeats itself, i.e. there is 75% (1.5 of every 2 meters) of space occupied by corridors and 25% (0.5 of every 2 meters) occupied by shelves, that is:[tex]Floor space_{shelves}=Total floor space*proportion of shelves=3500m^{2} *0.25=875m^{2}$

Knowing that every square meter of floor space occupied by shelves is in reality eight (because of being 8 shelves high) square meters of shelve space where to put books and that the average area of a book is

$Area occupied=depth*width=0.25m*0.05m=0,0125m^{2} per book$

Having all the necessary data, we estimate how many books would this college library hold:

$Books=\frac{Shelve space}{area_{book} } =\frac{875m^{2}*8 }{0.0125\frac{m^{2} }{book} } =560000 books$

As it is an estimate, we round it up to the nearest hundred-thousand, i.e., approximately [tex]6*10^{5}/tex] books can be shelved on this library