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Rates of change: inflated hot-air balloon

  1. Jun 10, 2013 #1
    1. The problem statement, all variables and given/known data
    An inflated hot air balloon can be considered as a perfect sphere woth diameter of 30m. When the hatch is opened, the hot air is lost at a rate of 118m^3/s. For the first 5 seconds, the balloon maintains its spherical shape, but then it begins to collapse. At what rate is the diameter decreasing after 3 seconds? How long does the balloon take to completely collapse?

    I know this is a chain rule question where dV/dt=118m^3/s and I'm not sure how to relate that to the diameter? I know that, because dV/dt is part of the equation the equation is either dV/dt=dV/dD*dD/dt where D is the diameter or the equation dD/dt=dD/dV*dV/dt or am I going about this the completely wrong way and have to get everything in terms of the radius?
  2. jcsd
  3. Jun 10, 2013 #2


    Staff: Mentor

    do you know the formula for the volume of a sphere in terms of the radius?
  4. Jun 10, 2013 #3
  5. Jun 10, 2013 #4


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    Staff Emeritus
    Science Advisor
    Homework Helper

    Then, what is the volume of a sphere in terms of its diameter?
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