Question

part a estimate how many books can be shelved in a college library with 3100 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 textbook, on average. express your answer using one significant figure.

Explanation:

Step1: Calculate shelf - available area

Let's assume a reasonable length for a shelf row. Say a shelf row is 10 m long. Total shelf - length per floor area unit: $(10\times8\times2)$ m (8 shelves high, 2 sides). Shelf - available area per unit area considering 1.5 m corridor: assume a 2 m wide section for shelves and corridor combined, so available shelf length per 2 m width is $10\times8\times2$ m.

Step2: Calculate number of books per unit area

If a book is 0.2 m thick, number of books per linear meter of shelf is $\frac{1}{0.2}=5$.

Step3: Calculate total number of books

Total number of 2 - m wide sections in 3100 $m^{2}$ is $\frac{3100}{2}$. Total number of books $N=\frac{3100}{2}\times10\times8\times2\times5$.
$N = 1.24\times10^{6}\approx1\times10^{6}$

Answer:

$1\times10^{6}$