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Application of derivative: a SPHERICAL balloon filled w gas has a leak that cause gas to escape at rate of 1.5m^3/min.?

At what rate is surface area shrinking when radius is 4m¿

1 Answer

  • 3 months ago
    Favorite Answer

    V = (4/3)πr³

    S = 4πr²

    We need to find the rate of the radius shrinking because

    dV/dt = dV/dr * dr/dt = 4πr² * dr/dt = -1.5m³/min

    dr/dt = -1.5/4πr²

    ds/dt = ds/dr * dr/dt = -8πr * 1.5/4πr² = -3/r m²/s

    -3/4 = -0.75m²/min 

    -0.75m²/60s * (100cm/1m)²= -125cm²/s <<<<<

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