Help Please! Attachments to come...

Question

anonymous · Answer

hi again

poofypenguin · Answer

Hello again! :D

poofypenguin · Answer

Here is my question:

anonymous · Answer

ah, more related rates

poofypenguin · Answer

Yep! Related rates! Here is my work so far...but i'm not sure where to go from here:

poofypenguin · Answer

It appears that the only thing i can do is sub in the two givens...but then i won't be able to solve for anything!

anonymous · Answer

The height is changing too, so you need to take the derivative of that as well

poofypenguin · Answer

oh whoops! let me give that a try!

anonymous · Answer

Oh, also, you want to know how fast something is changing, so you need to take the derivative with respect to time. You took the derivative of the Volume with respect to the height which isn't right

poofypenguin · Answer

ok...so that means that my initial formula isn't correct then...so i can't just use v=(1/3)pi*r^2*h?

anonymous · Answer

Sure, but then you have an extra variable to take the derivative of because the radius is changing as well

poofypenguin · Answer

So, what would be a better formula then? and how do you incorporate time? I'm not seeing it yet...

anonymous · Answer

Usually related rates is always with respect to time, because you want to know how fast something is changing.

You had it right the first time, except you want to differentiate with respect to a different variable:

$$\frac{dV}{dt} = \frac{1}{4} \pi h^2\frac{dh}{dt}$$

poofypenguin · Answer

Oooooh! I get it now! Let me give it a try!

poofypenguin · Answer

I got it wrong...can you check my work @math>philosophy ?

anonymous · Answer

Your algebra is off starting from the line where you use the V' notation. Don't skip steps. Remember you need to do to one entire side to the other entire side

poofypenguin · Answer

I keep looking at it but i keep getting the same answer! can you please be more specific?

anonymous · Answer

show the exact steps you are doing so i can see where you're going wrong

poofypenguin · Answer

My new work is similar to the one i just sent you, but i did it in more steps:

anonymous · Answer

it looks right actually. how do you know it's wrong?

poofypenguin · Answer

i'm doing an online assignment and it tells you if your answer is right or wrong..

poofypenguin · Answer

and in this case, for some reason it keeps telling me it's wrong...

anonymous · Answer

maybe it doesn't want an approximation? try leaving in the pi

poofypenguin · Answer

Wow! That worked! You're amazing! :D 
Thanks so much again!