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Implicit differentiation and related rates

  1. Nov 4, 2013 #1
    1. The problem statement, all variables and given/known data

    The spherical head of a snowperson is melting under the HOT sun at the rate of -160 cc/h (cubic centimetres per hour.) Find the rate at which the radius is changing when the radius r=16. Use cm/h for the units.
    (The volume of a sphere is given by V= 4π⋅r^3/3.)

    I have missed the past few calculus lectures and I am afraid I am falling behind, how would I start this kind of question? I know that the volume is changing at a rate of V - 160t where t is the number of hours...but I don't know how that helps at all.
     
  2. jcsd
  3. Nov 4, 2013 #2
    V = (4/3)πr3

    Differentiate both sides with respect to ‘t’ .What do you get ?
     
  4. Nov 4, 2013 #3
    dV/dt = 4πr^2*dr/dt
     
  5. Nov 4, 2013 #4
    Excellent...

    Now,dV/dt and 'r' is given to you .Just calculate dr/dt .
     
  6. Nov 4, 2013 #5
    Oh my (facepalm) thank you so much for the help!
     
  7. Nov 4, 2013 #6
    :thumbs:

    You are welcome :smile:
     
  8. Nov 4, 2013 #7
    If I was to do the same thing but instead I was given a volume and was looking for the rate of change of volume given the rate of change of radius, would I just isolate for r then take the derivative?
     
  9. Nov 5, 2013 #8
    That would be quite tedious .

    Instead, from the given volume just find out the radius using the relation V =(4/3)πr3 .Then approach in the similar manner .
     
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