Animating a Related-Rate Problem

July 15 2013 rlopez 1383

In a webinar on July 10, 2013, I solved the related rate problem:

Helium is pumped into a spherical balloon at the constant rate of 25 cu ft per min.
At what rate is the surface area of the balloon increasing at the moment when its radius is 8 ft?

A question in the Q&A at the end of the Webinar asked if it were possible to have an animation illustrate the expanding sphere and the rate of change in the surface area thereof. 

The Maple worksheet ( contains my response to this question. Clearly, it is easy enough to animate the expanding sphere, but what image captures the rate of change of the surface area?)

A recording of the webinar, "Related-Rates: Volume and Surface Area of a Sphere", is available for viewing online.

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