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!

Homework Help: Classic Related Rates: Sand Conical

  1. Oct 2, 2012 #1
    I've been trying to figure out where my mistake lies in the first solution. Some help would be appreciated. I did notice I got the same solution twice, so I assume I just calculated dr/dt twice and I need to use a different equation for dh/dt? Is dh/dt=(3/4)*dr/dt?

    1. Sand falls from a conveyor belt at a rate of 12 m^3/min onto the top of a conical
    pile. The height of the pile is always three-eights of the base diameter. How fast
    (in cm/min) are the height and the radius changing when the pile is 2m high.

    2. V=1/3πr2h
    r= 4/3h = 8/3
    h=3/4r = 2
    dv/dt= 12
    dh/dt= ?
    dr/dt = ?

    3. Solving for dh/dt /* Answer is incorrect*/
    12=(16/3)π(dh/dt) /*Plug in values and rearrange*/
    dh/dt=.7162 /* Proposed correction: Multiply by 3/4?*/

    Same for dr/dt /*Solution is Correct*/
    Last edited by a moderator: Oct 2, 2012
  2. jcsd
  3. Oct 2, 2012 #2


    Staff: Mentor

    It's important to keep in mind which things are constant, and which things are variable. V, r, and h are all changing with time, and the only thing that remains constant is dV/dt. Think of r = r(t), h = h(t), and V = V(t) as functions of t such that at a particular moment t0, r(t0) = 8/3, h(t0) = 2, and V(t0) = whatever it happens to be at that time.

    At any other time, r ≠ 8/3 and h ≠ 2.
    Use one or the other of these equations -- r = (4/3)h or h = (3/4)r to write V as a function of one variable alone.
  4. Oct 3, 2012 #3
    Thank you for your help.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook