Differential Calculus - Related Rates

[ruiwp13]

Homework Statement

A liquid is being filtrated by a filter with a cone form. The filtring tax is 2cm^3/min. The cone has 16cm height, 4 cm radius. The volume V is given by pi*r^2*y/2 where y is the height, r the radius. Discover a formula that relates the tax of variation of the liquid height with the height (y I guess).

Homework Equations

dV/dt = V*dh/dt
V=pi*r^2*y/3

The Attempt at a Solution

the volume is = pi*r^2*y/3

so Volume = pi.(4^2)*y/3

Volume=16*pi*y/3

dv/dt = 16*pi/3*dh/dt

-2 = 16*pi/3 dh/dt

dh/dt = -6/16*pi

But this solution is incorrect :/ Can anyone tell me where I missed?

Thanks in advance

 

[tiny-tim]

welcome to pf!

hi ruiwp13! welcome to pf!

(try using the X² button just above the Reply box )

the volume is = pi*r^2*y/3

so Volume = pi.(4^2)*y/3

nooo … r is a function of y, not fixed

so the volume is a multiple of y³

 

[ruiwp13]

hi ruiwp13! welcome to pf!

(try using the X² button just above the Reply box )


nooo … r is a function of y, not fixed

so the volume is a multiple of y³

didn't follow you there :/ what do you mean?

 

[tiny-tim]

the volume is a function of the radius (of the liquid surface) at time t, and the height at time t

the radius at time t is not 4, it depends the height

 

[ruiwp13]

the volume is a function of the radius (of the liquid surface) at time t, and the height at time t

the radius at time t is not 4, it depends the height

The maximum height being 16 and the radius 4 we can assume the radius y/4 or square(y)? is that it?

 

[tiny-tim]

yes, radius = y/4

 

[ruiwp13]

yes, radius = y/4

So now I have volume = pi*y*((y/4)^2)/3

volume = pi*y^3/48

dV/dt = pi*y^2/48 dy/dt

-2 = pi*y^2/48 dy/dt

dy/dt = 96*y^2/pi

still incorrect :/ I'm doing this exercise for a friend. I don't remember the subject that well. I'm doing something wrong or something missing probably. Sorry for the incovinience

 

[tiny-tim]

volume = pi*y^3/48

dV/dt = pi*y^2/48 dy/dt

nooo

 

[ruiwp13]

nooo

Is the formula that is incorrect? Because I don't have the formulas anymore... I'm helping a friend. I remembered it had something to do with related rates :p sorry to bother you

Or is it dV/dt = pi*3*y^2/48 dy/dt

Then -2 = pi*3*y^2/48 dy/dt

dy/dt = -96/pi*3*y^2

dy/dt = -32/pi*y^2 it's correct!

Thanks, a lot! Really helped me!

 

[tiny-tim]

Or is it dV/dt = pi*3*y^2/48 dy/dt

Yup!

(you knew that! )​

 

[ruiwp13]

Yup!

(you knew that! )​

Really, thank you! I appreciated that you didn't give me the answer and helped me get there "by myself". Really nice forum.