Question

A box measures 3.0 ft x 2.0 ft x 1.50 ft. Each book measures 25.0 cm x 10.0 cm x 5.0 cm. What is the maximum number of this books that this box can contain?

Answer 1

We will convert feet to centimeters by multiplying dimension in feet by k=30.48 cm/ft.

Volume of the box:

$$V_\text{cm}=kAkBkC=k^3ABC=\\ =30.48^3\cdot3\cdot2\cdot1.5=254851.6\text{ cm}^3.$$

Volume of a book:

$$v_\text{cm}=abc=\\ =25\cdot10\cdot5=1250\text{ cm}^3.$$

The integer part of the ratio "volume of the box" to "volume of one book" will be number of these books this box can contain is

$$n=\frac{V}{v}=\frac{254851.6}{1250}=203.88$$

Thus, the maximum number of books is 203.