The concentration of a biomolecule inside a rod-shaped prokaryotic cell is 0.0047 m. calculate the number of molecules inside the cell, which is 3.8 μm long and 1.6 μm in diameter.

First find the volume:

length = 3.8  um 
diameter =  1.6 um
so, radius = 1.6 / 2  = 0.8 um

so, volume =   
=  


1 um = 10^{-6} m
convert volume into m^3
so, = 

Now, Concentration is always in moles/Litre. So, we need to change the volume to litre.
1 m^3 = 10^{-3} L
So,

Now, number of moles =  concentration x volume 
=  

so no. of molecules =