How to find mass(mg) of cell wall that is 50nm thick and the cell itself is 2.0um in diameter ?

Question

the density of the cell wall is 1.00g/cm3

assume cell is spherical Volume = (4/3) pi r3

surface area= 4 pi r2

Answer 1

what you have is a spherical shell...a sphere with a small thickness

the way to find the volume of this is to take the surface area of the cell, 4 piR^2 and multiply by the thickness

if you know calculus, what you are doing is setting V=4/3 pi R^2

and realizing that dV=4 pi R^2 dR

dV is the element of volume of the shell, dR is the incremental thickness

so the volume of the shell is 4 pi (2x10^-6)^2 x 50x10^-9

(be sure to put everything in the same units)

and then the mass is just the density times the volume you just computed