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22 September, 22:26

The radius of a circle is increasing at a constant rate of 0.2 meters per second. what is the rate increase in the area of the circle at the instant when the circumference of the circle is 20π meters? v

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  1. 22 September, 22:41
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    Area of a circle, A = πr^2

    Therefore,

    dA/dt = 2πr. dr/dt, but dr/dt = 0.2

    Additionally,

    Circumference of a circle, C = 2πr

    Then, at C = 20π;

    20π = 2πr = > r = 20π/2π = 10

    At C = 20π;

    dA/dt = 2πr. dr/dt = 2π*10*0.2 = 4π m^2/s
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