Attachment 25033

Hi guys, i am having problem to solve the above question, i seem not able to get the correct answer each time i try out.

Hope someone could help me out. Thanks.

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- Oct 3rd 2012, 05:48 PMvetrifinding the rate of change of height of cone.
Attachment 25033

Hi guys, i am having problem to solve the above question, i seem not able to get the correct answer each time i try out.

Hope someone could help me out. Thanks. - Oct 3rd 2012, 06:24 PMMarkFLRe: finding the rate of change of height of cone.
Think of the volume $\displaystyle V$ of water in the conical container as being composed of circular disks of thickness $\displaystyle dh$. We may then state:

$\displaystyle \frac{dV}{dt}=\pi r^2\frac{dh}{dt}$

We know the ratio of the radius of the water's surface to the height of the water level will be the same as that of the container:

$\displaystyle r=\frac{2}{3}h$ hence:

$\displaystyle \frac{dV}{dt}=\pi \left(\frac{2}{3}h \right)^2\frac{dh}{dt}$

Now, solve for $\displaystyle \frac{dh}{dt}$ and use the given values of $\displaystyle \frac{dV}{dt},h$ to compute the requested value.