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A water tank is in the shape of a cone with vertical axis and vertex downward. The tank has a radius of 3m and is high 5m. At first the tank is full of water, but at time t=0 (in seconds), a small hole at the vertex is opened and the water begins to drain. When the height of the water in the tank has dropped to , the water is flowing out at a rate of 2m (cube)/s.
At what rate, in meters per seconds, is the water level dropping then?
I got this: dv/dt = 2m(cube)/s and we're looking for dh/dt.
We also know V=Pi(r^5)(h) /3 and r=3h/5.
However I don't know what to do afterwards
 one year ago
 one year ago
A water tank is in the shape of a cone with vertical axis and vertex downward. The tank has a radius of 3m and is high 5m. At first the tank is full of water, but at time t=0 (in seconds), a small hole at the vertex is opened and the water begins to drain. When the height of the water in the tank has dropped to , the water is flowing out at a rate of 2m (cube)/s. At what rate, in meters per seconds, is the water level dropping then? I got this: dv/dt = 2m(cube)/s and we're looking for dh/dt. We also know V=Pi(r^5)(h) /3 and r=3h/5. However I don't know what to do afterwards
 one year ago
 one year ago

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MarcLeclairBest ResponseYou've already chosen the best response.0
dw:1354523543605:dw
 one year ago

ShadowysBest ResponseYou've already chosen the best response.1
you can use \(\frac{dh}{dt}=\frac{dh}{dr} \times \frac{dr}{dV}\times \frac{dV}{dt}\) or just simply sub r=...h into V
 one year ago

ShadowysBest ResponseYou've already chosen the best response.1
do you need further help?
 one year ago

MarcLeclairBest ResponseYou've already chosen the best response.0
Sorry I hadn't seen the response, but after substituting r, i would find its derivative? And I don't get the first equation youve done :/
 one year ago

ShadowysBest ResponseYou've already chosen the best response.1
after subbing r, you'll get an eq where V is a function of h. the first eq is the chain rule lol for lazy people like me
 one year ago

MarcLeclairBest ResponseYou've already chosen the best response.0
how would that give you a function, that's where I always get confuse. I mean its just a volume equation :/ at a certain point in time
 one year ago

ShadowysBest ResponseYou've already chosen the best response.1
yup, that's the function, actually, that eq.
 one year ago

ShadowysBest ResponseYou've already chosen the best response.1
at that particular time where the time change is dt.
 one year ago

MarcLeclairBest ResponseYou've already chosen the best response.0
Ahhhhh its like as if the volume decrease, heigh decreases, so we could map a graph and therefore find its derivative.... ahaha thanks :)
 one year ago

ShadowysBest ResponseYou've already chosen the best response.1
lol you're welcome :)
 one year ago
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