in mitosis, each division forms 2 daughter cells.
this means that from a single cell, 2 daughter cells form.
when the 2 daughter cells divide, they form 4 cells in total (etc.)
this means that the general formula for the number of cells formed after a certain number of mitotic divisions is 2^n, where n is the number of divisions.
we are also told that the first division takes 24 hours, and the next few take 8 hours.
3 days is taken in total, which is 72 hours.
72h-24h = 48h
48h/8h = 6
this means that after 3 days, 1 24-hour cycle and 6 8-hour cycles will have taken place.
the total number of mitotic divisions in 3 days, then, is 1 + 6, which is 7.
using the general formula for the number of cells formed gives 2^7 cells, which is 128 cells.
the total volume is 4.2*10^-3 mm^3.
the total number of cells formed is 128.
hence, the mean volume of each cell is (4.2*10^-3)/(128) mm^3, which is 3.28125 * 10^-5 mm^3.