Question on cylinder calculation

[Rade]

I have this problem. Consider a cylinder

__________________
|________=________|

I shine a laser beam on the cylinder to view a field that has the dimensions of (=) being 500 microns x 500 microns. The cylinder is say100,000 microns in length, 5,000 in width. I determine that 5 objects of R exist within the field of view of each (=) area for the entire cylinder. What is calculus equation that I should use to determine total number of R objects on the entire outside area of the cylinder ? Thanks for any help (ps/ not a homework question, a research question).

 

[HallsofIvy]

I have this problem. Consider a cylinder

__________________
|________=________|

I shine a laser beam on the cylinder to view a field that has the dimensions of (=) being 500 microns x 500 microns. The cylinder is say100,000 microns in length, 5,000 in width. I determine that 5 objects of R exist within the field of view of each (=) area for the entire cylinder. What is calculus equation that I should use to determine total number of R objects on the entire outside area of the cylinder ? Thanks for any help (ps/ not a homework question, a research question).

For a cylinder of length L, width W (the diameter of the cylinder), the are of the curved portion (Excluding the two ends. It's not clear whether you are including them or not) has area $\pi LW$ (If you do intend to include the ends, the total area is $\pi LW+ \pi\frac{W^2}{2}$). Divide that area by the area of your field of view (250000 square microns) and multiply by 5. I see no reason to use calculus.

 

[Rade]

For a cylinder of length L, width W (the diameter of the cylinder), the are [sic--"arc"] of the curved portion (Excluding the two ends. It's not clear whether you are including them or not) has area $\pi LW$ (If you do intend to include the ends, the total area is $\pi LW+ \pi\frac{W^2}{2}$). Divide that area by the area of your field of view (250000 square microns) and multiply by 5. I see no reason to use calculus.

Thank you very much. Yes, I do wish to include both ends of the arc in this calculation. If you have the time, I have one more question--a variation of the above. Suppose I view only the leading edge of the "arc" of the cylinder one (=) section at a time, such as this over time:

start |=--------| , |-=------| , |--=-----|, |---=----|, etc,|-------=| end

I rotate the cylinder 10 degrees and do the count again, rotate another 10 degress and count. I calculate that the statistical mean number of R objects/ (=) area is equal to 5. What equation is used to estimate the total number of R objects on the cylinder (assume the new field of view for each (=) area is now 10 microns x 500 microns) ? Thanks again for any help provided.