Optimization Quick Problem

Hello guys, quick question. I'm attempting to optimize the surface area of a frustum but I'm having trouble understanding how to get from one step to another. Could anyone please explain why this person chose to change the variables (r,R,h) and how they deduced the substitutions? Here's the link:

https://math.stackexchange.com/questions/4024363/optimizing-a-conical-frustum-using-partial-differentiation/4024472#4024472
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Thanks

  • So you just need an explanation for the change the variables (r,R,h) and how the substitution is done?

  • Yes, I need the explanation for the change of variables, and why he chose those values. It just seems kind of random to throw sin and cos in there, and I haven't been able to find an explanation for it.

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