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28 December, 14:11

Suppose that, for the sphere in the video, instead of being told how fast the radius is changing, we're told that the volume is increasing at a constant rate of d V d t = 4 cubic centimeters per second. How fast is the radius increasing at the instant when the radius is r = 10 centimeters? d r d t =

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  1. 28 December, 14:20
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    3.185 x 10^-3 cm/s

    Explanation:

    dV / dt = 4 cubic cm per second

    r = 10 cm

    The volume of sphere is given by

    V = 4/3 x π x r³

    Differentiate both sides with respect to t

    dV / dt = 4/3 x π x 3r² x dr/dt

    Put dV / dt = 4 cubic cm per second, r = 10 cm

    4 = 4/3 x 3.14 x 3 x 10 x 10 x dr/dt

    dr/dt = 3.185 x 10^-3 cm/s
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