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28 January, 00:36

A helium balloon ride lifts up passengers in a basket. Assume the density of air is 1.28 kg/m3 and the density of helium in the balloon is 0.18 kg/m3. The radius of the balloon (when filled) is R = 4.5 m. The total mass of the empty balloon and basket is mb = 123 kg and the total volume is Vb = 0.068 m3. Assume the average person that gets into the balloon has a mass mp = 74 kg and volume Vp = 0.077 m3. What is the volume of helium in the balloon when fully inflated?

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  1. 28 January, 00:41
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    V = 381.70 m³

    Explanation:

    ρ air = 1.28 kg / m³

    ρ helium = 0.18 kg / m³

    R = 4.5 m

    Vb = 0.068 m³

    mb = 123 kg

    To determine the volume of helium in the balloon when fully inflated

    V = 4 / 3 π * R ³

    V = 4 * π / 3 (4.5 m) ³

    V = 381.70 m³

    To determine the mass total

    m = ρ helium * V

    m = 0.18 kg / m³ * 381.70 m³

    m = 68.70 kg

    mt = (68.70 + 123) kg

    mt = 191.70 kg
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