How to find equation of stairs up a cone(I need help)

HighSchoolStress

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Sep 18, 2020
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Hi I am doing IB and I am doing a math EE. a topic of exploration is how a logarithmic spiral can be used to model a line with constant slope going up a cone. I heard it can be a logarithmic spiral because it had a derivative that is constant. what i mean is when you look at a cone from the side, the slope of the line will be constant and had a 20 degree angle with the xy plane. if anyone has any idea on how to do this please help i am in desperate need of help. Also the example was thinking about is a cone with a radius of 100 units and height of 100 units. I got r= e^0.364(theta). it does not fit with a paper diagram i drew.
 
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