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Homework Help: Implicit Differentiation of Cylinder NOT given radius?

  1. Apr 7, 2008 #1
    Implicit Differentiation of Cylinder NOT given radius????

    1. The problem statement, all variables and given/known data

    Question: Digging in his backyard, Dennis accidentally breaks a pipe attached to his water sprinkling system. water bubbles up at a rate of 1 cm^3/s, forming a circular pond of depth 0.5cm in his yard. How quickly is the surface area of the pond covering his lawn?

    Given: dV/dT= 1
    depth= 0.5cm

    RTF: dSA/Dt

    2. Relevant equations

    V= pi&r^2&h
    SA= 2pi&r&h + 2pi&r^2

    3. The attempt at a solution

    i attempted alot of things...i just always end up with the same problem: i dont know what r is or i cant find a way to relate r to anything.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Apr 7, 2008 #2
    you don't actually need r at all.

    [tex] V=Sh[/tex] this is the formula for calculating the volume of a cylindrical shape right? S- surface area, h- depth.
    Use this info to find [tex] \frac{dS}{dt}[/tex] using the info you were given.
  4. Apr 7, 2008 #3


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    Homework Helper

    Welcome to PF!

    Hi banfill_89! Welcome to PF! :smile:

    First, you've missed out one relevant equation … what is V in terms of t?

    And your SA equation is wrong … you're asked how fast the lawn is being covered. so you don't need the sides of the cylinder. And it's πr^2, not 2πr^2.
    You have two equations for r … so you solve for r in the V equation (that is, you put "r =" on the left), and then you substitute that value of r into the SA equation.

    You now have an SA equation with t but no r! :smile:
  5. Apr 7, 2008 #4

    agh thanks alot guys. i was heading in that direction too but my surface area equation was screwing me up. thanks for puttin me in the right direction
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