Question

I'm really struggling to figure this question out.
Let V be the volume of a cylinder having height h and radius r, assume that h and r vary with time.
a.) How are dV/dt, dh/dt, and dr/dt related?

Answer 1

this is the continued question from part a.)
\[\frac{ dV }{ dt }=f(r,h)\frac{ dh }{ dt }+g(r,h)\frac{ dr }{ dt } where f(r,h)=? and g(r,h)=?\]

Answer 2

You should start out stating the volume of a cylinder.

Answer 3

Since we want to know how dV/dt,dh/dt, and dr/dt relate
We will differentiate the equation the volume of a cylinder.

Answer 4

I differentiated and got
\[V=\pi(r^2\frac{ dh }{ dt }+2rh \frac{ dr }{ dt })\]
I'm just not sure what to do after this