Math Arguments

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 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?