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20 November, 13:26

Show that the maximum rate of change, with respect to radius, of the volume of a deflating balloon is four times the sphere's initial great circle circumference

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  1. 20 November, 15:56
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    Step-by-step explanation:

    Let's say R is the initial radius of the sphere, and r is the radius at time t.

    The volume of the sphere at time t is:

    V = 4/3 π r³

    Taking derivative with respect to radius:

    dV/dr = 4π r²

    This is a maximum when r is a maximum, which is when r = R.

    (dV/dr) max = 4π R²

    This is 4 times the sphere's initial great circle area, but not the great circle circumference. The problem statement contains an error.
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