Differentials and Rates of Change; Related Rates

[Qube]

Homework Statement

http://i4.minus.com/jboxzSadIJVVoi.jpg

Homework Equations

Product rule; implicit differentiation.

Volume of cylinder, V = pi(r^2)(h)

The Attempt at a Solution

dV/dt = 0 = pi[2r(dr/dt)(h) + (dh/dt)(r^2)]

Solve the equation after plugging in r = 5; h = 8, and dh/dt = -2/5. Solve for dr/dt.

0 = 80pi(dr/dt) - 10pi

1 = 8(dr/dt)

dr/dt = 1/8

 

[elvishatcher]

You are not trying to find $\frac{dr}{dt}$. Each part of the question wants you to find $\frac{dV}{dt}$ for a given rate at which the radius is changing (think about what represents the rate of change of the radius).

 

[iRaid]

You are not trying to find $\frac{dr}{dt}$. Each part of the question wants you to find $\frac{dV}{dt}$ for a given rate at which the radius is changing (think about what represents the rate of change of the radius).

It says to find the rate of change of the radius in the first part of the question.

I think you just have to have it like this: $\frac{dV}{dt}=2\pi r\frac{dr}{dt}\frac{dh}{dt}$, then just plug in values.

Edit: Oh forgot to add, the V is constant, so what does that mean the value of dV/dt is?

 

[haruspex]

You are not trying to find $\frac{dr}{dt}$. Each part of the question wants you to find $\frac{dV}{dt}$ for a given rate at which the radius is changing (think about what represents the rate of change of the radius).

It's multiple choice. V is given as constant, dh/dt is a given value, so the obvious approach is to calculate dr/dt and see which choice matches. Of course, you could run it the other way: for each choice compute dV/dt and see which one gives 0, but that probably takes longer on average.

the dV/dt is constant, so what does that mean the value of it is?

You mean V is constant, so what value is dV/dt, right?

 

[iRaid]

It's multiple choice. V is given as constant, dh/dt is a given value, so the obvious approach is to calculate dr/dt and see which choice matches. Of course, you could run it the other way: for each choice compute dV/dt and see which one gives 0, but that probably takes longer on average.

You mean V is constant, so what value is dV/dt, right?

Yes, my mistake.

 

[Qube]

Is 1/8 the correct answer? I've redone the work again below:

 

[Qube]

 

[haruspex]

Is 1/8 the correct answer? I've redone the work again below:

Yes.