1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Related rates question involving volume of cone

  1. Nov 21, 2014 #1
    1. The problem statement, all variables and given/known data

    Sand falls from a conveyor belt at the rate of 10m^3/min onto the top of a conical pile. The height of the pile is always 3/8ths of the base diameter.

    How fast is the radius changing when the pile is 4 m high?


    3. The attempt at a solution

    V = pir^2 (4/3) -- volume of a cone

    dv/dt = (4pi/3)(2r)(dr/dt)
    10 = (4pi/3)(2)(16/3)(dr/dt)
    10 = (128pi/9)(dr/dt)
    dr/dt = 0.224


    The answer is 0.1119 m/sec. What am I doing wrong?
     
  2. jcsd
  3. Nov 21, 2014 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    You might want to confirm this formula for the volume of a cone. Remember, volume has units of L3, and there are units of L2 here. There is also no accounting for the height of the cone in this formula.
     
  4. Nov 21, 2014 #3
    The formula is correct I just mislabelled it. I meant to say that V = pir^2 (4/3) -- volume of a cone when h = 4.
     
  5. Nov 21, 2014 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Might be right (I did not check the prefactor), but the height is not constant. It changes together with r. You cannot consider one change and ignore the other one.
     
  6. Nov 21, 2014 #5

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The volume of a cone is ##V=\frac 1 3 \pi r^2 h##. You must avoid putting in the instantaneous values before you differentiate to get the related rates equation.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Related rates question involving volume of cone
Loading...