The equation for solving the Volume of a Cylinder is a simple middle school equation: V= πr2h, where h = height and r= radius.
The equation can also be written in “multi variable form: f(r, h)=πr2h. This allows us to work with partial derivatives if either h or r are held constant. The most common real world application that I feel this would be very useful would be in any facility where chemicals are handled frequently. I imagine engineers in those facilities could use these kind of equations to measure chemical additions but also simple inventory. Having worked with chemicals in a previous job I have seen where it is very common to receive the same chemicals in different sized containers and also having to adapt to those changes.
With respect to the radius of a cylinder, height is held constant:
f(r, h)=πr2h can be written fr=π(2r)h or fr=2πrh , meaning that as long as the height is held constant, any change to the radius = 2πrh.
With respect to the height of a cylinder, radius is held constant (probably seen more in practical use):
f(r, h)=πr2h can be written fh=πr2(1) or fh=πr2 , meaning that as long the radius is held constant, any change to the height = πr2.
After wrapping this up, it does seem a bit simpler than some of the rest of the class posts, but it made sense to me having worked with the application in the past. Hopefully I am on the right track and look forward to any feedback.
References:
https://www.mathsisfun.com/calculus/derivatives-partial.html
