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posted by  UserLiz on 10/20/2009 7:40:36 PM  |  status: Closed  |  Earned Karma: 12

Need Help Asap, please!! Derivatives and related rates

Course Textbook Chapter Problem Needs by
Calculus Calculus (5th) by Stewart 3.9 2E 10/20/2009 at 11:30:00 PM
Question Details:
2.a. If A is the area of a circle with radius r and the circle expands as time passes, find  dA/dt in terms of dr/dt.
So I have,  A= π r 2
           dA/dt = 2π r (dr/dt)
2.b. Suppose oil spills from a ruptured tanker and spreads in a circular pattern.  If the radius of the oil spill increases at a constant rate of  1m/s, how fast is the area of the spill increasing when the radius is 30m?
So far, I have that I need to find    dA/dt      and that  dr/dt = 1m/s       and that r =30m
I set up this equation:       dA/dt= π (30)2
                                       dA/dt= 900π  
or am I supposed to plug it into dA/dt= 2π (30) (1)    <<<<<<from the equation of part a.      ???
Could someone please help me and point me in the right direction!?  thank you so much!
Liz

AAnswers:

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Oracle
Karma Points: 14,954
posted by Grace on 10/20/2009 7:47:37 PM  |  status: Live
Asker's Rating: Lifesaver   
Response Details:
Good work on part a. Use that knowledge in part b.

2b) want: rate of area (dA/dt) when r = 30 m
relationship: A = πr2
   so dA/dt = 2πr(dr/dt) from part a
   dA/dt = 2π(30)(1) = 60π m2/s

You want to use dA/dt and not go back to the A relationship since you want to find dA/dt.
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