Looking thru a microscope if there are x number of an an object seen
how do I calculate how many there would be per sq.cm. if the magnification
was 400 and the diameter 490 ? (The x nos. are 16 and 31)

Hello whitbyoz, here is how I would solve your problem:

First convert the 490 micrometers into centimeters. To do this you
multiply micrometers by 1 x 10^-4 or 490 micrometers equals .049
centimeters. This is the diameter of your field of view.

Next calculate the area of your field of view using:

Area = pi d^2 / 4 

Area = 3.1416 (.049)^2 / 4 = .0018857 cm^2

Then your formula becomes:

Number per sq.cm. = X / .0018857 

For X = 16

Number per sq.cm = 16 / .0018857 = 8,485

For X = 31

Number per sq.cm = 31 / .0018857 = 16,439

If there is any of this you don't understand, please ask and I will try and help.

Easy to follow and an answer that made sense. Many Thanks