Raffle roll

Suppose you have a roll of raffle tickets who's outer radius is R and
the inner radius (the dowel) is r. Given the length of a ticket, l,
and it's width w, what is the formula that could be used to calculate
the number of tickets in the roll?

I'm drawing a blank on this one. I can't seem to think of an integral
that would work for this problem.

 

By w you mean the thickness of a ticket I guess? Rather than looking at
integrals, you can look at areas when viewed from the end, i.e. looking
along the direction of the dowel. You know the area between the outer and
inner radii, and the area of a single ticket...

Regards,
Mike.

 

That seems like a good approach. However, it would seem that finding
the total volume of the raffle roll and dividing it by the volume of a
single ticket would be the way to go with that.

 

Well finding either an accurate volume or an accurate thickness for a ticket
would not be easy to do directly - I can only think that you would produce a
roll with a known number of tickets, and calculate the volume of the roll,
then divide by number of tickets. Having done this once, however, you could
use the result for calculating the number of tickets in different size
rolls...