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math

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A spherical ball is being filled with air. When the radius r=7cm, the radius is increasing at a rate 2 cm/s. How fast is the volume changing at this time (leave your answer approximate)?

  • math -

    V = (4/3)πr^3
    dV/dt = 4πr^2 dr/dt

    when r = 7 , dr/st = 2

    dV/dt = 4π(49)(2) = 392π cm^3/sec
    = appr 1231.5

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