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21 July, 16:38

How much longer does it take to inflate a balloon to a diameter of 28 inches instead of a diameter of 7 inches. assume the rate that air enters is constant?

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  1. 21 July, 16:58
    0
    When inflating the balloon to a diameter of 7 inches, the final volume is

    V₁ = (4/3) π * (7/2 in) ³ = 57.1667π in³

    When inflating the balloon to a diameter of 28 in, the final volume is

    V₂ = (4/3) π * (28/2 in) ³ = 3658.7π in³

    If the rate of air entry into the balloon is constant, then

    V₂/V₁ = 3658.7/57.1667 = 64

    Answer: it takes 64 times longer.
  2. 21 July, 17:02
    0
    It takes 64 times longer to inflate a balloon to a diameter of 28 inches instead of a diameter of 7 inches.
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