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.