Question 212578
First an Angstrom = 1 ten billionth of a meter.  That is 1/10,000,000,000 of a meter.  (By the way, I didn't know that!  I had to look it up!!)


The oil is going to form what is essentially a "cylinder" as it spreads out in a circle, with a radius, and a VERY small thickness (or height!).  What you want to find is the height of the cylinder, given that the volume is 1 cubic millimeter and the AREA of the circle is 1 square meter.


The formula for the volume of a cylinder is V = Area * Height.

In this case, it will be V=Area*Thickness, where V=1 cu mm, A=1 sq m, Thickness = x, the unknown.


In order to get the same units, convert 1 cu mm to cu m.  First 1 mm = .001 m, so 1 mm^3 = .001^3 m^3.  In scientific notation {{{(10^-3)^3=10^-9}}}


V=Area*Thickness
1 cu mm = 10^-9 cu m = 1 sq m  * x m


Turn it around!  It will look better:

{{{1 sq m *x m = 10^(-9)}}} cu m

{{{x= 10^(-9) }}} m   (Square meters divides into cubic meters leaving meters for the correct unit!)


Now convert this to Angstroms, where 1 Angstrom = 10^-10 meters.  


Multiply both sides of the above equation by 10:
10 Angstroms = 10* 10^-10 meters = 10^-9, and that is exactly what you have!


10 Angstroms should be the final answer.  Wow!  Where did you get THAT problem???  Somebody send me an email if I'm wrong!!


R^2


Dr. Robert J. Rapalje, Semi-retired
Seminole Community College
Altamonte Springs, FL  32714