Question

Related Rates:
how are dv/dt, dr/dt, and dh/dt related?
dv/dt= f(r,h)dh/dt+g(r,h)dr/dt, where f(r,h)=? and g(r,h)=?
how do I figure out f(r,h) and g(r,h)??
I know V=πr^2h and
dv/dt= 2πrh*dr/dt +πr^2*dh/dt

In part b.) At a certain instant, the height is 8 in and increasing at 1 in/s, while the radius is 11 in and decreasing at 1 in/s. How fast is the volume changing at that instant? Is the volume increasing or decreasing at that instant? I got dv/dt=-55π in^3/s

I just need help with the f(r,h) and g(r,h)

Answer 1

well if you found
dv/dt correctly that should answer your question of what is f(r,h) and g(r,h)

Answer 2

compare to find

Answer 3

\[\frac{dv}{dt}=(2 \pi r h) \frac{dr}{dt}+(\pi r^2) \frac{dh}{dt} \\ \frac{dv}{dt}=g(r,h)\frac{dr}{dt}+f(r,h)\frac{dh}{dt}\]

Answer 4

If V = pi*r^2h how do you get dV/dt? what rule or rules do you need to use?

Answer 5

thanks i finally understood it