The area of a circle is increasing at a rate of 4ft /min.How fast is the radius of this circle increasing at the instant the area is 16π ft?

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  • 1 month ago

    Area (A) of a circle is = π R²  where R = radius of the circle.

    =>  A  =  π R²

    When Area  =  16π,  R = 4 ft  ......................... (1)

    Differentiate both the sides with respect to Time (t),

    dA/dt = 2 π R dR/dt

    dA = Rate of change in area = 4 ft² /min  and Radius =  4 ft ..... (from 1 above )

    =>  Rate of change in Area  =  ( 2 π R ) *  Rate in change of Radius.

    =>  4  =  2 π 4 ( dR/dt)

    => dR/dt  =  1/(2π)  ft/min ........ Answer

  • dA/dt = 4

    A = pi * r^2

    dA/dt = 2 * pi * r * dr/dt

    A = 16 * pi

    16 * pi = pi * r^2

    16 = r^2

    4 = r

    dA/dt = 2 * pi * r * dr/dt

    4 = 2 * pi * 4 * dr/dt

    1/(2pi) = dr/dt

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