Sunday, November 22, 2015

505: The Balloon Problem

We've all seen this problem, but many of our students haven't.  It's the related rate problem from calculus: the balloon being filled with air.

There are two questions being demonstrated here.
(1) "If the volume increases at a constant rate, what is happening to the radius?" and
(2) "If the radius increases at a constant rate, what is happening to the volume?"

The first question is to figure out which situation is modeled in red and which in blue.
Then we can ask:
  • Does the radius increase at a constant speed in both models? How can you tell?
  • Does the volume increase at a constant speed in both models? How can you tell?
  • Where or how, in the RealWorldtm, could we see the constant increase in volume?
  • Where or how, in the RealWorldtm, could we see the constant increase in radius?

If you want to play with the animation, Balloon Problem. source: @k8nowak

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