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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Physics

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24 October, 16:14

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)

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Allen Olson · Answer 1

It takes 64 times longer to inflate a balloon to a diameter of 28 inches instead of a diameter of 7 inches.

Rex Holt · Answer 2

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.