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!

Differentiation application problem

  1. May 1, 2016 #1
    1. The problem statement, all variables and given/known data
    An inverted cone has a depth of 10cm and a base radius of 5cm. Water is poured into it at the rate of 1.5 cm^3/ min. Find the rate at which level of water in the cone is rising, when the depth of water is 4cm.

    2. Relevant equations


    3. The attempt at a solution

    I know that this question requires the application of chain rule. However having only recently studied it, I am yet to fully understand it's application. Therefore looking for an answer which gives a correct approach to such questions.

    Thanks.
     
  2. jcsd
  3. May 1, 2016 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Well, PF doesn't provide answers to members, only guidance. You must try harder to understand the question.

    For example, how would you calculate the volume of water in this cone, given the depth of the water?
     
  4. May 1, 2016 #3
    Ok, so what I've done is this -

    In the ques. h=2r or r=h/2
    So the formula for volume of cone is written in terms of 'h'.

    Now,
    dv/dt = 1.5 (given)
    And dv/dh is calculated.

    Then after applying chain rule, dh/dt comes out to be 3/8π

    Now could you please tell me if I'm right?
    Thanks
     
  5. May 1, 2016 #4

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Is this (3/8)π or 3/(8π)?
     
  6. May 1, 2016 #5

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    As SteamKing notes, that is technically (3/8)π, but maybe you did not mean that. Either way, I get a different answer. Please post your working.
     
  7. May 1, 2016 #6
    Volume of cone = 1/3π r2h
    r=5 cm. h = 10 cm
    r= h/2

    1/3π (h2/4) h

    πh3/12

    dv/dt = 1.5
    dh/dt = ?

    dv/dt = dh/dt * dv/dh
    1.5 = dh/dt * πh2/4

    dh/dt = 6/πh2

    Now putting h=4,
    I got the answer 3/(8π)
     
  8. May 1, 2016 #7
    The height of the cone is not 4 cm, that is the starting depth of the water, and not the height of the cone.
     
  9. May 1, 2016 #8

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    You should write complete equations in your work, rather than isolated expressions.

    For example, write

    V = πh3/12 rather than just πh3/12

    It makes your thoughts much easier to follow in extended calculations.
     
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: Differentiation application problem
Loading...