A balloon (in a shape of a sphere) is inflated with helium at a constant rate of 125 cm^3/s. Calculate the rate of increase of the diameter when the volume is 2000 cm^3.

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  1. V = (4/3)π r^3
    dV/dt = 4π r^2 dr/dt

    when V = 2000
    (4/3)πr^3 = 2000
    r^3 = 1500/π
    r = (1500/π)^(1/3)
    = 7.8159... I stored in my calculator's memory

    so in
    dV/dt = 4π r^2 dr/dt
    125 = 4π (7.8159...)^2 dr/dt
    dr/dt = .1628618

    rate of change of diameter = .3225536 cm/s

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