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 RealWorld
^{tm}, could we see the constant increase in volume?
- Where or how, in the RealWorld
^{tm}, could we see the constant increase in radius?

If you want to play with the animation,

Balloon Problem. source:

@k8nowak