Results 1 to 5 of 5

Math Help - related rates

  1. #1
    Newbie
    Joined
    Jul 2008
    Posts
    16

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by zintore View Post
    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
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2008
    Posts
    16
    Quote Originally Posted by Jhevon View Post
    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?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by zintore View Post
    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.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2008
    Posts
    16
    Quote Originally Posted by Jhevon View Post
    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?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Related Rates
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 26th 2009, 09:54 PM
  2. Rates and Related Rates!!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 2nd 2008, 11:53 AM
  3. Another Related Rates
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 13th 2008, 07:32 AM
  4. Related Rates
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 12th 2008, 06:49 PM
  5. rates and related rates
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 29th 2007, 10:51 PM

Search Tags


/mathhelpforum @mathhelpforum