Chapter 1, Problem 25P

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 1.5m wide. Assume books are about the size of this one, on average.

To determine

Number of books that can be shelved in a college library.

Answer to Problem 25P

Solution: The number of books that can be shelved in a college library of ${\text{3500 m}}^{\text{2}}$ is $8.75\times {10}^5$ books.

Explanation of Solution

Assume each book is 20 cm deep and 4 cm wide. First, one needs to estimate how much floor space a book occupies and estimate how much floor space a shelf requires.

If one shelf has books on both sides, it should be 50 cm (0.5m) deep. This means that 8 shelves occupy:

   depth

Therefore, all shelves cover ${\frac{1}{4}}^{\text{th}}$ of the floor space as corridors occupy 1.5 m width.

  

Now, one book covers a floor space of:

  

Therefore, the number of books ( $n_b$ ) in one shelf is:

  $\begin{array}{l}{n}_b=\frac{\text{875}{\text{m}}^{\text{2}}}{\text{0}\text{.008}{\text{m}}^{\text{2}}}\\ {\text{n}}_b\text{=109375}\end{array}$

Finally, the total number of books ( $n_{tot,b}$ ) that can be occupied in 8 shelves is:

  

Conclusion:

Assuming that each book has $\text{20 cm}$ depth and $\text{4 cm}$ width, the number of books that can be shelved in a college library of ${\text{3500 m}}^{\text{2}}$ is $8.75\times {10}^5$ books.