# Thread: related rates

1. ## related rates

A chemical storage tank is in the shape of an inverted cone with depth 12 meters and top radius 5 meters. When the depth of the chemical in the tank is 1 meter, the level is falling at 0.1 meters per minute. How fast is the volume of chemical changing?

so V= 1/3 pi r^2 h
dh/dt=.1 at h=1 and r=5/12 is what i can gather..
i also got dV/dt= 1/3 pi r^2 dh/dt + 2/3 pi r h dr/dt --- IF i use this equation , how do i find dr/dt

or if i use dV/dt= dV/dh * dh/dt how do i find dV/dh

2. Originally Posted by zintore
A chemical storage tank is in the shape of an inverted cone with depth 12 meters and top radius 5 meters. When the depth of the chemical in the tank is 1 meter, the level is falling at 0.1 meters per minute. How fast is the volume of chemical changing?

so V= 1/3 pi r^2 h
dh/dt=.1 at h=1 and r=5/12 is what i can gather..
i also got dV/dt= 1/3 pi r^2 dh/dt + 2/3 pi r h dr/dt --- IF i use this equation , how do i find dr/dt

or if i use dV/dt= dV/dh * dh/dt how do i find dV/dh
we are not given any information about r or dr/dt, so finding them directly is futile. instead, get rid of r all together.

note that r = (5/12)h. see post #3 here for the method on how to obtain this.

so replace r with (5/12)h and continue, you won't need to know what dr/dt is

3. Originally Posted by Jhevon
we are not given any information about r or dr/dt, so finding them directly is futile. instead, get rid of r all together.

note that r = (5/12)h. see post #3 here for the method on how to obtain this.

so replace r with (5/12)h and continue, you won't need to know what dr/dt is
so then i get V= 25/432 pi h^3
dV/dt= (75pi*h^2)/ 432 * dh/dt
dV/dt|h=1 = 5pi/288

can someone confirm?

4. Originally Posted by zintore
so then i get V= 25/432 pi h^3
dV/dt= (75pi*h^2)/ 432 * dh/dt
you're right, up to here

dV/dt|h=1 = 5pi/288
not sure what you are saying here. are you saying, "dV/dt when h = 1 is..."? if so, nope

can someone confirm?
you're off. firstly, dh/dt = -0.1. it is negative because it is decreasing.

5. Originally Posted by Jhevon
you're right, up to here

not sure what you are saying here. are you saying, "dV/dt when h = 1 is..."? if so, nope

you're off. firstly, dh/dt = -0.1. it is negative because it is decreasing.
so.. is the answer -5pi/288?