another rate of change problem.

Sep 2008
631
2
A hallow rigght circular cone has height 18cm and base radius 12cm. It is held vertex downwards beneath a tap leaking at the rate of \(\displaystyle 2 cm^{3} s^{-1} \)

Find the rate of rise of water level when the depth is 6cm.
I have no idea how to start this, I know that \(\displaystyle V = \frac{1}{3} \pi r^{2} h \)

any help appreciated,

thanks
 
May 2010
2
2
London
Well, you are looking for an expression for dh/dt...once you have this you can substitute 6 for h for your answer.

You have V in terms of r and h. First use the fact that the ratio of r to h stays constant to find a formula for V in terms of h only. Then you can calculate dV/dh.

You are given dV/dt, so no you can use the chain rule to find dh/dt.
 
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Sep 2008
631
2
Well, you are looking for an expression for dh/dt...once you have this you can substitute 6 for h for your answer.

You have V in terms of h, so you can calculate dV/dh. And you are given dV/dt.

Now use the chain rule to find dh/dt.

thanks,

The thing I am getting confused with is that we are not given dv/dt. the \(\displaystyle 2cm^{3} s^{-1} \) does not represent the depth of the cone, that's just the rate that the water is dripping from the tap.

so how can you usethe value for dv/dt?

thanks
 
May 2010
2
2
London
is a measure of volume per second, which is the rate of change of volume over time, ie dV/dt=2.
 
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Apr 2010
384
153
Canada
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