Answer
The average size of a brain cell entirely filled with water would be 10$^{-15}$ m$^3$. If the brain cells were simple cubes the length of one side of one cell would be 10$^{-5}$. Finally, if the cells were spread out in a one cell layer per page through the book it would cover 1750 pages.
Work Step by Step
Because the average brain cell weighs 10${^9}$ g and 1 g of water 1 ml (1 cm$^3$), the volume of a cell entirely filled with water would be 10$^{-15}$ m$^3$. The equation to get this solution is the weight of an average brain cell multiplied by 1 g of water, which would be 10$^{-9}$ g X 10$^{-6}$ m$^3$/g. If the take the cube root of this answer we get the length of one side of a brain cell if it were a cube. Finally, the surface of the page in this book is 0.057 m$^2$ (21 cm X 27.5 cm). The cell footprint is 10$^{-10}$ m$^2$. If we divide the the cell footprint by the calculated surface, we get the equation 57 X 10$^7$. The solution for this equation is the amount of cells that would fit on one page. So, the final equation would be 10$^{12}$/[57 X 10$^7$]), which gives us 1750, the number of pages.
