Implicit Differentiation: Find dh/dr Using the Volume of a Cone Formula

This video provides an example of how to perform implicit differentiation.

[ninolatimer]

Why did you add in the value of the volume then derive and not radius or height? I tried deriving first without entering any value in so using v=(1/3)πr^2h and it didn't go so well. Did you only not enter radius and height since we are trying to find the change in height with respect to the radius?

Edit: If you wanted to find change in volume with respect to radius, after finding dh/dr=-10, could I then go back and this time take the derivative with r instead of 5cm^3, and this time enter -10 for dh/dt? I got -15πcm^2 but of course it should be cubed

[numerical]

What is the purpose of the volume value?