Rates of change: inflated hot-air balloon

  • #1

Homework Statement


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?
 

Answers and Replies

  • #2
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do you know the formula for the volume of a sphere in terms of the radius?
 
  • #4
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
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Then, what is the volume of a sphere in terms of its diameter?
 

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