Question

A certain person had a brain that weighed 1.10 kg and contained 3.51 x 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.

If the surface were spread out into a thin layer that was a single cell thick what would be the surface area in square meters?

Answer 1

brain weight = 1.10 kg = 1.1 x 1000 g = 1100 g

number of cells in brain = 3.51 x 10^10

each cell weight = 1100 / 3.51 x 10^10

                           = 3.134 x 10^-8 g

density of water = 1 g / cm^3

that means 1 g of water in 1 cm^3 or ml

here

1 g cell occupies = 1cm^3 volume

3.134 x 10^-8 g = 3.134 x 10^-8 cm^3 volume

volume of cell = 3.134 x 10^-8 cm^3

cell is cubic = in cubic cell = side ^3

side ^3 = 3.134 x 10^-8 cm^3

side = 3.152 x 10^-3 cm = 0.032 cm

length of side of the cell = 0.0032 cm

area = side x side = 0.0032 x 0.0032 = 1.024 x 10^-5

area = 1.024 x 10^-5 cm^2

1 m^2 = 10^4 cm^2

area = 1.024 x 10^-5 cm^2

        =1.024 x 10^-5 x 10^-4 m^2

        = 1.024 x 10^-9 m^2

for each cell area = 1.024 x 10^-9 m^2

total cells surface area = 3.51 x 10^10 x 1.024 x 10^-9

                                  = 35.94 m^2