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31 December, 23:15

Air is being blown into a spherical balloon at the rate of 1.68 in. 3/s. Determine the rate at which the radius of the balloon is increasing when the radius is 4.70 in. Assume that π = 3.14.

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  1. 31 December, 23:44
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    Answer: 0.006in/s

    Explanation:

    Let the rate at which air is being blown into a spherical balloon be dV/dt which is 1.68in³/s

    Also let the rate at which the radius of the balloon is increasing be dr/dt

    Given r = 4.7in and Π = 3.14

    Applying the chain rule method

    dV/dt = dV/dr * dr/dt

    If the volume of the sphere is 4/3Πr³

    V = 4/3Πr³

    dV/dr = 4Πr²

    If r = 4.7in

    dV/dr = 4Π (4.7) ²

    dV/dr = 277.45in²

    Therefore;

    1.68 = 277.45 * dr/dt

    dr/dt = 1.68/277.45

    dr/dt = 0.006in/s
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