1. Not finding help here? Sign up for a free 30min 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!

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

    tiny-tim

    User Avatar
    Science Advisor
    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
    thanks

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Implicit Differentiation of Cylinder NOT given radius?
Loading...