Constants:
- The horizontal length of the paper roll will not change as it unrolls;
- The inner cylindrical empty space is present with radius r
- Paper roll has a radius R measured from the center of the empty space in the middle to the edge of the roll
- The roll is being unrolled at a constant rate, however the change in volume and radius R isn't constant
What I know:
- I started off by differentiating the formula for the volume of a cylinder with radius R. I ignored the empty space in the middle with radius r as it is a constant and will disappear during differentiation
- After differentiating what I got was $\frac{dV}{dt} = 2\pi hR(\frac{dR}{dt})$
- However none of the $dt$ functions are constant therefore I cant have an experiment just measuring the radius or the volume over time to find the $dt$ functions value as the other $dt$ function will affect it.
Question:
What is another way that I could approach this problem mathematically to have a constant rate of change for any of the variables listed above or a new variable like the length of the paper that has been unrolled which will increase constantly that has not been talked above. Or is there a way to manipulate the existing variables to at least plot a graph for one of the them?
Any help is appreciated.