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19 March, 09:06

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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Answers (2)
  1. 19 March, 12:03
    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. 19 March, 12:59
    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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