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Related Rates Clay Pot Problem

  1. Nov 5, 2013 #1
    1. The problem statement, all variables and given/known data

    A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder increases and the radius, r decreases. If the length of the cylinder is increasing at 0.1 cm per second, find the rate at which the radius is changing when the radius is 1 cm and the length is 5 cm.

    2. Relevant equations

    N/A

    3. The attempt at a solution

    So I know that dL/ds=0.1. But I don't know exactly how the radius changes as L changes. I'm having trouble setting up a function for this. If I had that I could do the rest of the problem.
     
  2. jcsd
  3. Nov 5, 2013 #2

    Dick

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    The volume is constant as the potter rolls. What's an equation for the volume of a cylinder in terms of the radius and length?
     
  4. Nov 5, 2013 #3
    V=Lπr2

    But how can I connect this with time?
     
  5. Nov 5, 2013 #4

    Dick

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    Differentiate both sides d/dt.
     
  6. Nov 5, 2013 #5
    How can I differentiate this function with respect to time?
     
  7. Nov 5, 2013 #6

    Dick

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    V is a constant. r and L are both functions of time. Write V=πr(t)^2*L(t). Now differentiate it.
     
  8. Nov 5, 2013 #7
    Thank you I think I figured it out:

    dV/dt=2L(t)πr(t)r'(t)+L'(t)πr(t)2
    0=2L(t)πr(t)r'(t)+L'(t)πr(t)2
    0=2L(t)r'(t)+L'(t)r(t)
    2L(t)r'(t)=-L'(t)r(t)
    r'(t)=-L'(t)r(t)/2L(t)r'(t)
    r'(t)=-0.1(1)/2(5)
    r'(t)=-0.1/10=-0.01cm/s
     
  9. Nov 6, 2013 #8

    Dick

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    Right. Well done.
     
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