Conversion Question !!?

Question

A human tissue cell has a diameter of the order 1.0 micrometer. Assuming each cell occupies a cube of 1.0 micrometer on one side; estimate the number of cells in .5 cubic centimeter of tissue

please explain each step...

Answer 1

1 micrometer=10^(-4)centimeter

You want to find how many cubic micrometers are in .5 cubic centimeters, i.e. you divide: .5cm^3 by 1 cubic micrometer.

You use this conversion factor:

[ micometer/(10^(-4)centimeter) ] ^ 3 which is equal to 1 since the numerator and denominator are the same, i.e. (x/x)^y is always 1, that is, in this case, micrometer= 10^(-4)centimeter=x and y=3.

So you have

[(.5centimeter^3)/( 1 micrometer ^ 3 ) ] times
[micrometer/(10^(-4) centimeter ) ] ^ 3 = .5/{[10^(-4)]^3} =
.5/[10^(-12)] =

.5x10^12 cells or 500,000,000,000 cells

The units centimeter^3 and micrometer^3 cancel out since they are on both the top and bottom and you are left with the number of cells. Conversion factors always equal to 1.

Answer 2

Actually a human tissue cell is quite a bit larger than this.
1 cubic micrometre is approximately the size of some
spherical bacteria such as staphylococci & streptococci.

In linear measure, there are 1,000,000 micrometres in 1 metre.
That means there are 10,000 micrometres in 1 centimetre.
So if you now cube both of those, it works out that there are
10,000^3 = 10^12 cubic micrometres in 1 cubic centimetre.
So there will be half that in 0.5 cubic centimetres.
Half of 10^12 = 5*10^11 or 500,000,000,000 cubic micrometres.
So if each cell occupies 1 cubic micrometre, then there
will be 500,000,000,000 cells in the sample of tissue.

Answer 3

maybe you should read a book on the matter.