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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?

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  1. Area = πr^2
    d(area)/dt = 2πr dr/dt
    but dr/dt = 1 m/s

    d(area)/dt = 2π(30)(1) = 60π m^2/s

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