Calculus

a spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. how fast is the radius of the balloon increasing at the instant the radius is 30 centimeters?

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  1. The vloume increase rate is dV/dt = 500
    V = (4/3) pi R^3
    dV/dt = (12/3)pi R^2 dR/dt
    = 4 pi R^2 dR/dt

    You can use that equation to compute the dR/dt expansion rate for any value of R.

    Note that that dV/dt equals the instantaneous surface area times dR/dt.

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  2. r=30cm
    500=4 pi R^2 dR/dt
    500=11309.7336 dR/dt
    dR/dt = .0442cm/min

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