Rates of change question

Question is confusing as I don't know what formula I should use for a cylindrical tank and it says find rate of fluid in proportion to square root of V, though I am meant to show it satisfies an equation with the square root of h?

dV/dt = dV/dh dh/dt

Do I use V= 1/3(pi)(r)^2(h)?
If so then dV/dt = 2/3(pi)(r)(h) x dh/dt
Then what?

you do but note r is constant, h is varying

How does knowing that help me?

I do not understand what is the problem.

I'm still confused, how exactly am I satisfying dh/dt by using dv/dt?
Do I need to re-arrange v into h=3V/(pi)(r)^2 and sub that into -k(V)^1/2 which I then put into dv/dt?

Are you happy with post 2?

no, I'm still confused. I'd rather you tell me the answer as I don't have it in the book I am using

no, I'm still confused. I'd rather you tell me the answer as I don't have it in the book I am using

I would of course tell you the answer but some people here do not like this.
I will look into my resources to find the most similar worked example to yours if you give me 5 minutes

this is the closest match I can find
Hopefully this will help you with yours
All the best

Thanks! I'm assuming you can only do v = Ah instead of 1/3(pi)(r)^2h in "show that" type questions or can you use it in other rate of change questions?

in your question you have V = 1/3(pi)r²h
but your dV/dh = 1/3(pi)r² = constant which you can absorb into k