Question

A certain person had a brain that weighed 1.20 kg and contained 4.63 × 10^10 cells. Assuming that each cell was completely filled with water (density = 1.00 g/mL), calculate the length of one side of such a cell if it were a cube.

____ cm

If the cells were spread out into a thin layer that was a single cell thick, what would be the total surface area (in square meters) for one side of the cell layer?

____ m2

Answer 1

Given that, mass of brain = 1.20 kg =1200 g

Number of cells = 4.63 *10¹⁰

So, Mass of each cell = Mass of brain/total number of cells = 1200g /(4.63 *10¹⁰) = 2.59 *10^-8 g

Now, cells are completely filled with water

So, mass of each cell = Mass of water in each cell = 2.59 *10^-8 g

Cell volume = Mass/ density = (2.59 *10^-8 g)/ 1.00g/mL = 2.59 *10^-8 mL

But cell volume = a³ = 2.59 *10^-8 mL

a = 2.96 *10^-3 mL = 2.96 *10^-3 cm . [ 1mL = 1cm]

Surface area of cell = 6a² = 6 * (2.59 *10^-3 )² = 5.25 *10^-5 cm² = 5.25 *10^-9 m²

Hence total surface area for one side of the cell layer = Surface area of a cell * Total number of cells =

5.25 *10^-9 cm² * 4.63 *10¹⁰ = 243.18 m²