Chapter 1, Problem 25P

(II) 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 about the size of this one, on average.

The textbook is approximately 25 cm deep and 5 cm wide. With books on both sides of a shelf, the shelf would need to be about 50 cm deep. If the aisle is 1.5 meter wide, then about 1/4 of the floor space is covered by shelving. The number of books on a single shelf level is then $\frac{1}{4}\left(3500{\text{m}}^2\right)\left(\frac{1\text{ book}}{(0.25\text{ m})(0.05\text{ m})}\right)=7.0\times {10}^4$ books. With 8 shelves of books, the total number of books stored is as follows.

$\left(7\times {10}^4\frac{\text{ books}}{\text{shelf level}}\right)(8\text{ shelves})\approx 6\times {10}^5\text{ books}$