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zeesbrat3
 one year ago
A water filter has the shape of an inverted right circular cone with base radius 3 meters and height 9 meters. Water is being pumped into the filter at the rate of 10 meters3/sec. Find the rate, in meters/sec, at which the water level is rising when the water is 3 meters deep.
zeesbrat3
 one year ago
A water filter has the shape of an inverted right circular cone with base radius 3 meters and height 9 meters. Water is being pumped into the filter at the rate of 10 meters3/sec. Find the rate, in meters/sec, at which the water level is rising when the water is 3 meters deep.

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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Hey! related rates problem

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436729337203:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436729438553:dw

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0What's the next step?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1I miss these problems, so fun. What we're given is \[\frac{ dV }{ dt } = 10\frac{ m^3 }{ s }\] and you have to find \[\frac{ dh }{ dt }\] ganeshie used similar triangles above to find r so we can use the volume formula \[V = \frac{ 1 }{ 3 }\pi \left( \frac{ h }{ 3 } \right)^2h = \frac{ 1 }{ 9 }\pi h^3\] now we differentiate!!

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0So.. \[\frac{ dv }{dt? } = \frac{ 1 }{ 3 }pih^2\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ dV }{ dt } = \frac{ \pi }{ 3 }h^2 \frac{ dh }{ dt }\] notice we differentiate respect to t

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Remember we are using the chain rule here, sorry @ganeshie8 for intruding hehe I just like these problems :D

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Now we solve for \[\frac{ dh }{ dt }\] can you go ahead and try that please

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0here is my reasoning: dw:1436729996057:dw we can write: \[\Large \begin{gathered} dV = \pi {r^2}dh \hfill \\ \hfill \\ \frac{{dV}}{{dt}} = \pi {r^2}\frac{{dh}}{{dt}} \hfill \\ \hfill \\ \frac{{dV}}{{dt}} = \pi {\left( {\frac{h}{3}} \right)^2}\frac{{dh}}{{dt}} \hfill \\ \hfill \\ \frac{{dV}}{{dt}} = \frac{{\pi {h^2}}}{9}\frac{{dh}}{{dt}} \hfill \\ \hfill \\ \frac{{dV}}{{dt}} = \frac{\pi }{{27}}\frac{{d\left( {{h^3}} \right)}}{{dt}} \hfill \\ \end{gathered} \]

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0\[10 = \frac{ 1 }{ 3 }\pi(9)^2\frac{ dh }{ dt }\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ dh }{ dt } = \frac{ 3 }{ \pi h ^2 } \frac{ dV }{ dt }\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ dh }{ dt } = \frac{ 3 }{ \pi(3)^2 } \times 10 = \frac{ 30 }{ 9 \pi ^2 }\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1That is the rate of water rising

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0So \[\frac{ 30 }{ 88.7364 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The answer is 3.18. Astrophysics is wrong on so many levels.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1@dahmanman show your work and I might believe you.
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